SUMOylation is a posttranslational modification (PTM) at a lysine residue and is crucial for the proper functions of many proteins, particularly of transcription factors, in various biological processes. Zinc finger homeobox 3 (ZFHX3), also known as AT motif-binding factor 1 (ATBF1), is a large transcription factor that is active in multiple pathological processes, including atrial fibrillation and carcinogenesis, and in circadian regulation and development. We have previously demonstrated that ZFHX3 is SUMOylated at three or more lysine residues. Here, we investigated which enzymes regulate ZFHX3 SUMOylation and whether SUMOylation modulates ZFHX3 stability and function. We found that SUMO1, SUMO2, and SUMO3 each are conjugated to ZFHX3. Multiple lysine residues in ZFHX3 were SUMOylated, but Lys-2806 was the major SUMOylation site, and we also found that it is highly conserved among ZFHX3 orthologs from different animal species. Using molecular analyses, we identified the enzymes that mediate ZFHX3 SUMOylation; these included SUMO1-activating enzyme subunit 1 (SAE1), an E1-activating enzyme; SUMO-conjugating enzyme UBC9 (UBC9), an E2-conjugating enzyme; and protein inhibitor of activated STAT2 (PIAS2), an E3 ligase. Multiple analyses established that both SUMO-specific peptidase 1 (SENP1) and SENP2 deSUMOylate ZFHX3. SUMOylation at Lys-2806 enhanced ZFHX3 stability by interfering with its ubiquitination and proteasomal degradation. Functionally, Lys-2806 SUMOylation enabled ZFHX3-mediated cell proliferation and xenograft tumor growth of the MDA-MB-231 breast cancer cell line. These findings reveal the enzymes involved in, and the functional consequences of, ZFHX3 SUMOylation, insights that may help shed light on ZFHX3's roles in various cellular and pathophysiological processes.

In cyanobacteria, metabolic pathways that use the nitrogen-rich amino acid arginine play a pivotal role in nitrogen storage and mobilization. The N-terminal domains of two recently identified bacterial enzymes: ArgZ from Synechocystis and AgrE from Anabaena, have been found to contain an arginine dihydrolase. This enzyme provides catabolic activity that converts arginine to ornithine, resulting in concomitant release of CO2 and ammonia. In Synechocystis, the ArgZ-mediated ornithine–ammonia cycle plays a central role in nitrogen storage and remobilization. The C-terminal domain of AgrE contains an ornithine cyclodeaminase responsible for the formation of proline from ornithine and ammonia production, indicating that AgrE is a bifunctional enzyme catalyzing two sequential reactions in arginine catabolism. Here, the crystal structures of AgrE in three different ligation states revealed that it has a tetrameric conformation, possesses a binding site for the arginine dihydrolase substrate l-arginine and product l-ornithine, and contains a binding site for the coenzyme NAD(H) required for ornithine cyclodeaminase activity. Structure–function analyses indicated that the structure and catalytic mechanism of arginine dihydrolase in AgrE are highly homologous with those of a known bacterial arginine hydrolase. We found that in addition to other active-site residues, Asn-71 is essential for AgrE's dihydrolase activity. Further analysis suggested the presence of a passage for substrate channeling between the two distinct AgrE active sites, which are situated ∼45 Å apart. These results provide structural and functional insights into the bifunctional arginine dihydrolase–ornithine cyclodeaminase enzyme AgrE required for arginine catabolism in Anabaena.

Philip Newsholme
Dec 1, 2006; 55:S39-S47
Section II: The Muscle and Liver Connections

Lena Eliasson
May 1, 2020; 69:804-812
Small Noncoding RNAs in Diabetes

Sarah M. Gray
Dec 1, 2014; 63:3992-3997
Perspectives in Diabetes

Gordon C. Weir
Dec 1, 2004; 53:S16-S21
Section I: Insulin Resistance-Beta-Cell Connection in Type 2 Diabetes

Gunnar Stenström
Dec 1, 2005; 54:S68-S72
Section II: Type 1-Related Forms of Diabetes

VOLUME 295 (2020) PAGES 1898–1914Yichen Zhong's name was misspelled. The correct spelling is shown above.

Cindy J.M. Loomans
Jan 1, 2004; 53:195-199
Complications

Thomas A. Buchanan
Sep 1, 2002; 51:2796-2803
Pathophysiology

Steven E Kahn
Nov 1, 1993; 42:1663-1672
Original Article

David E. Kelley
Oct 1, 2002; 51:2944-2950
Metabolism and Signal Transduction

Permanent neonatal diabetes mellitus (PNDM) is caused by reduced β-cell number or impaired β-cell function. Understanding of the genetic basis of this disorder highlights fundamental β-cell mechanisms. We performed trio genome sequencing for 44 patients with PNDM and their unaffected parents to identify causative de novo variants. Replication studies were performed in 188 patients diagnosed with diabetes before 2 years of age without a genetic diagnosis. EIF2B1 (encoding the eIF2B complex α subunit) was the only gene with novel de novo variants (all missense) in at least three patients. Replication studies identified two further patients with de novo EIF2B1 variants. In addition to having diabetes, four of five patients had hepatitis-like episodes in childhood. The EIF2B1 de novo mutations were found to map to the same protein surface. We propose that these variants render the eIF2B complex insensitive to eIF2 phosphorylation, which occurs under stress conditions and triggers expression of stress response genes. Failure of eIF2B to sense eIF2 phosphorylation likely leads to unregulated unfolded protein response and cell death. Our results establish de novo EIF2B1 mutations as a novel cause of permanent diabetes and liver dysfunction. These findings confirm the importance of cell stress regulation for β-cells and highlight EIF2B1’s fundamental role within this pathway.

Obesity-associated type 2 diabetes mellitus (T2DM) entails insulin resistance and loss of β-cell mass. Adipose tissue mitochondrial dysfunction is emerging as a key component in the etiology of T2DM. Identifying approaches to preserve mitochondrial function, adipose tissue integrity, and β-cell mass during obesity is a major challenge. Mitochondrial ferritin (FtMT) is a mitochondrial matrix protein that chelates iron. We sought to determine whether perturbation of adipocyte mitochondria influences energy metabolism during obesity. We used an adipocyte-specific doxycycline-inducible mouse model of FtMT overexpression (FtMT-Adip mice). During a dietary challenge, FtMT-Adip mice are leaner but exhibit glucose intolerance, low adiponectin levels, increased reactive oxygen species damage, and elevated GDF15 and FGF21 levels, indicating metabolically dysfunctional fat. Paradoxically, despite harboring highly dysfunctional fat, transgenic mice display massive β-cell hyperplasia, reflecting a beneficial mitochondria-induced fat-to-pancreas interorgan signaling axis. This identifies the unique and critical impact that adipocyte mitochondrial dysfunction has on increasing β-cell mass during obesity-related insulin resistance.

Central to the development of diabetic macro- and microvascular disease is endothelial dysfunction, which appears well before any clinical sign but, importantly, is potentially reversible. We previously demonstrated that hyperglycemia activates nuclear factor of activated T cells (NFAT) in conduit and medium-sized resistance arteries and that NFAT blockade abolishes diabetes-driven aggravation of atherosclerosis. In this study, we test whether NFAT plays a role in the development of endothelial dysfunction in diabetes. NFAT-dependent transcriptional activity was elevated in skin microvessels of diabetic Akita (Ins2^+/–) mice when compared with nondiabetic littermates. Treatment of diabetic mice with the NFAT blocker A-285222 reduced NFATc3 nuclear accumulation and NFAT-luciferase transcriptional activity in skin microvessels, resulting in improved microvascular function, as assessed by laser Doppler imaging and iontophoresis of acetylcholine and localized heating. This improvement was abolished by pretreatment with the nitric oxide (NO) synthase inhibitor l-N^G-nitro-l-arginine methyl ester, while iontophoresis of the NO donor sodium nitroprusside eliminated the observed differences. A-285222 treatment enhanced dermis endothelial NO synthase expression and plasma NO levels of diabetic mice. It also prevented induction of inflammatory cytokines interleukin-6 and osteopontin, lowered plasma endothelin-1 and blood pressure, and improved mouse survival without affecting blood glucose. In vivo inhibition of NFAT may represent a novel therapeutic modality to preserve endothelial function in diabetes.

Diabetic retinopathy (DR) is a widespread vision-threatening disease, and neuroretinal abnormality should be considered as an important problem. Brain-derived neurotrophic factor (BDNF) has recently been considered as a possible treatment to prevent DR-induced neuroretinal damage, but how BDNF is upregulated in DR remains unclear. We found an increase in hydrogen peroxide (H₂O₂) in the vitreous of patients with DR. We confirmed that human retinal endothelial cells secreted H₂O₂ by high glucose, and H₂O₂ reduced cell viability of MIO-M1, Müller glia cell line, PC12D, and the neuronal cell line and lowered BDNF expression in MIO-M1, whereas BDNF administration recovered PC12D cell viability. Streptozocin-induced diabetic rats showed reduced BDNF, which is mainly expressed in the Müller glia cell. Oral intake of eicosapentaenoic acid ethyl ester (EPA-E) ameliorated BDNF reduction and oscillatory potentials (OPs) in electroretinography (ERG) in DR. Mass spectrometry revealed an increase in several EPA metabolites in the eyes of EPA-E–fed rats. In particular, an EPA metabolite, 18-hydroxyeicosapentaenoic acid (18-HEPE), induced BDNF upregulation in Müller glia cells and recovery of OPs in ERG. Our results indicated diabetes-induced oxidative stress attenuates neuroretinal function, but oral EPA-E intake prevents retinal neurodegeneration via BDNF in Müller glia cells by increasing 18-HEPE in the early stages of DR.

Primary hyperparathyroidism (PHPT) is a common endocrine disorder, definitive treatment usually requiring surgical removal of the offending parathyroid glands. To perform focused surgical approaches, it is necessary to localize all hyperfunctioning glands. The aim of the study was to compare the efficiency of established conventional scintigraphic imaging modalities with emerging ¹⁸F-fluorocholine PET/CT imaging in preoperative localization of hyperfunctioning parathyroid glands in a larger series of PHPT patients. Methods: In total, 103 patients with PHPT were imaged preoperatively with ¹⁸F-fluorocholine PET/CT and conventional scintigraphic imaging methods, consisting of ^99mTc-sestamibi SPECT/CT, ^99mTc-sestamibi/pertechnetate subtraction imaging, and ^99mTc-sestamibi dual-phase imaging. The results of histologic analysis, as well as intact parathyroid hormone and serum calcium values obtained 1 d after surgery and on follow-up, served as the standard of truth for evaluation of imaging results. Results: Diagnostic performance of ¹⁸F-fluorocholine PET/CT surpassed conventional scintigraphic methods (separately or combined), with calculated sensitivity of 92% for PET/CT and 39%–56% for conventional imaging (65% for conventional methods combined) in the entire patient group. Subgroup analysis, differentiating single and multiple hyperfunctioning parathyroid glands, showed PET/CT to be most valuable in the group with multiple hyperfunctioning glands, with sensitivity of 88%, whereas conventional imaging was significantly inferior, with sensitivity of 22%–34% (44% combined). Conclusion: ¹⁸F-fluorocholine PET/CT is a diagnostic modality superior to conventional imaging methods in patients with PHPT, allowing for accurate preoperative localization.

Kathleen Melhuish & Kristen Lew Texas State University “[Functions] are completely different, which is what makes this course so challenging.” – Abstract Algebra Student Functions are hard for students, even students in abstract algebra courses. Even if students have seen … Continue reading →

Elizabeth H. Harris
Jul 1, 2005; 23:115-119
Feature Articles

Neelima V. Chu
Jan 1, 2001; 19:
Practical Pointers

OBJECTIVE

In children with type 1 diabetes (T1D), severe hypoglycemia (SH) is associated with poorer cognition, but the association of SH with cognitive function in late life is unknown. Given the increasing life expectancy in people with T1D, understanding the role of SH in brain health is crucial.

Angelo Avogaro
May 1, 2011; 34:S285-S290
Hypertension

TODAY Study Group
Jun 1, 2013; 36:1749-1757
TODAY Study

OBJECTIVE

To assess functional β-cell capacity in type 2 diabetes during 2 years of remission induced by dietary weight loss.

OBJECTIVE

To confirm the presence of subclinical cardiovascular dysfunction in working-age adults with type 2 diabetes (T2D) and determine whether this is improved by a low-energy meal replacement diet (MRP) or exercise training.

OBJECTIVE

To compare the risk of lactic acidosis hospitalization between patients treated with metformin versus sulfonylureas following development of reduced kidney function.

OBJECTIVE

The aim of this study was to examine the association of circulating retinol-binding protein 4 (RBP4) levels with β-cell function across the spectrum of glucose tolerance from normal to overt type 2 diabetes.

OBJECTIVE

To evaluate the impact of once-weekly exenatide (EQW) on microvascular and cardiovascular (CV) outcomes by baseline renal function in the Exenatide Study of Cardiovascular Event Lowering (EXSCEL).

OBJECTIVE

Diabetes is a major risk factor for renal function decline and failure. The availability of multiplex panels of biochemical markers provides the opportunity to identify novel biomarkers that can better predict changes in renal function than routinely available clinical markers.

OBJECTIVE

Previous studies suggested that childhood prediabetes may develop prior to obesity and be associated with relative insulin deficiency. We proposed that the insulin-deficient phenotype is genetically determined and tested this hypothesis by longitudinal modeling of insulin and glucose traits with diabetes risk genotypes in the EarlyBird cohort.

Stuttgart : F. Enke, 1883.

Braunschweig : Druck und Verlag von Friedrich Vieweg und Sohn, 1898.

Hannover : Köllner, 1898.

London : Bailliere, Tindall, & Cox, 1880.

England : London County Council, Public Assistance Department, 1935.

Rockville, Maryland : National Institute on Drug Abuse, 1986.

Wei Li, Subhashis Ghosal.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1707--1743.

Abstract:
A filament consists of local maximizers of a smooth function $f$ when moving in a certain direction. A filamentary structure is an important feature of the shape of an object and is also considered as an important lower dimensional characterization of multivariate data. There have been some recent theoretical studies of filaments in the nonparametric kernel density estimation context. This paper supplements the current literature in two ways. First, we provide a Bayesian approach to the filament estimation in regression context and study the posterior contraction rates using a finite random series of B-splines basis. Compared with the kernel-estimation method, this has a theoretical advantage as the bias can be better controlled when the function is smoother, which allows obtaining better rates. Assuming that $f:mathbb{R}^{2}mapsto mathbb{R}$ belongs to an isotropic Hölder class of order $alpha geq 4$, with the optimal choice of smoothing parameters, the posterior contraction rates for the filament points on some appropriately defined integral curves and for the Hausdorff distance of the filament are both $(n/log n)^{(2-alpha )/(2(1+alpha ))}$. Secondly, we provide a way to construct a credible set with sufficient frequentist coverage for the filaments. We demonstrate the success of our proposed method in simulations and one application to earthquake data.

Tomáš Rubín, Victor M. Panaretos.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 1137--1210.

Abstract:
Functional time series analysis, whether based on time or frequency domain methodology, has traditionally been carried out under the assumption of complete observation of the constituent series of curves, assumed stationary. Nevertheless, as is often the case with independent functional data, it may well happen that the data available to the analyst are not the actual sequence of curves, but relatively few and noisy measurements per curve, potentially at different locations in each curve’s domain. Under this sparse sampling regime, neither the established estimators of the time series’ dynamics nor their corresponding theoretical analysis will apply. The subject of this paper is to tackle the problem of estimating the dynamics and of recovering the latent process of smooth curves in the sparse regime. Assuming smoothness of the latent curves, we construct a consistent nonparametric estimator of the series’ spectral density operator and use it to develop a frequency-domain recovery approach, that predicts the latent curve at a given time by borrowing strength from the (estimated) dynamic correlations in the series across time. This new methodology is seen to comprehensively outperform a naive recovery approach that would ignore temporal dependence and use only methodology employed in the i.i.d. setting and hinging on the lag zero covariance. Further to predicting the latent curves from their noisy point samples, the method fills in gaps in the sequence (curves nowhere sampled), denoises the data, and serves as a basis for forecasting. Means of providing corresponding confidence bands are also investigated. A simulation study interestingly suggests that sparse observation for a longer time period may provide better performance than dense observation for a shorter period, in the presence of smoothness. The methodology is further illustrated by application to an environmental data set on fair-weather atmospheric electricity, which naturally leads to a sparse functional time series.

Emilio Porcu, Rachid Senoussi, Enner Mendoza, Moreno Bevilacqua.

Source: Electronic Journal of Statistics, Volume 14, Number 1, 890--916.

Abstract:
The paper considers reduction problems and deformation approaches for nonstationary covariance functions on the $(d-1)$-dimensional spheres, $mathbb{S}^{d-1}$, embedded in the $d$-dimensional Euclidean space. Given a covariance function $C$ on $mathbb{S}^{d-1}$, we chase a pair $(R,Psi)$, for a function $R:[-1,+1] o mathbb{R}$ and a smooth bijection $Psi$, such that $C$ can be reduced to a geodesically isotropic one: $C(mathbf{x},mathbf{y})=R(langle Psi (mathbf{x}),Psi (mathbf{y}) angle )$, with $langle cdot ,cdot angle $ denoting the dot product. The problem finds motivation in recent statistical literature devoted to the analysis of global phenomena, defined typically over the sphere of $mathbb{R}^{3}$. The application domains considered in the manuscript makes the problem mathematically challenging. We show the uniqueness of the representation in the reduction problem. Then, under some regularity assumptions, we provide an inversion formula to recover the bijection $Psi$, when it exists, for a given $C$. We also give sufficient conditions for reducibility.

Mahalanobis distance is a classical tool in multivariate analysis. We suggest here an extension of this concept to the case of functional data. More precisely, the proposed definition concerns those statistical problems where the sample data are real functions defined on a compact interval of the real line. The obvious difficulty for such a functional extension is the non-invertibility of the covariance operator in infinite-dimensional cases. Unlike other recent proposals, our definition is suggested and motivated in terms of the Reproducing Kernel Hilbert Space (RKHS) associated with the stochastic process that generates the data. The proposed distance is a true metric; it depends on a unique real smoothing parameter which is fully motivated in RKHS terms. Moreover, it shares some properties of its finite dimensional counterpart: it is invariant under isometries, it can be consistently estimated from the data and its sampling distribution is known under Gaussian models. An empirical study for two statistical applications, outliers detection and binary classification, is included. The results are quite competitive when compared to other recent proposals in the literature.

Consider an unknown smooth function $f: [0,1]^d ightarrow mathbb{R}$, and assume we are given $n$ noisy mod 1 samples of $f$, i.e., $y_i = (f(x_i) + eta_i) mod 1$, for $x_i in [0,1]^d$, where $eta_i$ denotes the noise. Given the samples $(x_i,y_i)_{i=1}^{n}$, our goal is to recover smooth, robust estimates of the clean samples $f(x_i) mod 1$. We formulate a natural approach for solving this problem, which works with angular embeddings of the noisy mod 1 samples over the unit circle, inspired by the angular synchronization framework. This amounts to solving a smoothness regularized least-squares problem -- a quadratically constrained quadratic program (QCQP) -- where the variables are constrained to lie on the unit circle. Our proposed approach is based on solving its relaxation, which is a trust-region sub-problem and hence solvable efficiently. We provide theoretical guarantees demonstrating its robustness to noise for adversarial, as well as random Gaussian and Bernoulli noise models. To the best of our knowledge, these are the first such theoretical results for this problem. We demonstrate the robustness and efficiency of our proposed approach via extensive numerical simulations on synthetic data, along with a simple least-squares based solution for the unwrapping stage, that recovers the original samples of $f$ (up to a global shift). It is shown to perform well at high levels of noise, when taking as input the denoised modulo $1$ samples. Finally, we also consider two other approaches for denoising the modulo 1 samples that leverage tools from Riemannian optimization on manifolds, including a Burer-Monteiro approach for a semidefinite programming relaxation of our formulation. For the two-dimensional version of the problem, which has applications in synthetic aperture radar interferometry (InSAR), we are able to solve instances of real-world data with a million sample points in under 10 seconds, on a personal laptop.

The accuracy and complexity of kernel learning algorithms is determined by the set of kernels over which it is able to optimize. An ideal set of kernels should: admit a linear parameterization (tractability); be dense in the set of all kernels (accuracy); and every member should be universal so that the hypothesis space is infinite-dimensional (scalability). Currently, there is no class of kernel that meets all three criteria - e.g. Gaussians are not tractable or accurate; polynomials are not scalable. We propose a new class that meet all three criteria - the Tessellated Kernel (TK) class. Specifically, the TK class: admits a linear parameterization using positive matrices; is dense in all kernels; and every element in the class is universal. This implies that the use of TK kernels for learning the kernel can obviate the need for selecting candidate kernels in algorithms such as SimpleMKL and parameters such as the bandwidth. Numerical testing on soft margin Support Vector Machine (SVM) problems show that algorithms using TK kernels outperform other kernel learning algorithms and neural networks. Furthermore, our results show that when the ratio of the number of training data to features is high, the improvement of TK over MKL increases significantly.

We present new excess risk bounds for general unbounded loss functions including log loss and squared loss, where the distribution of the losses may be heavy-tailed. The bounds hold for general estimators, but they are optimized when applied to $eta$-generalized Bayesian, MDL, and empirical risk minimization estimators. In the case of log loss, the bounds imply convergence rates for generalized Bayesian inference under misspecification in terms of a generalization of the Hellinger metric as long as the learning rate $eta$ is set correctly. For general loss functions, our bounds rely on two separate conditions: the $v$-GRIP (generalized reversed information projection) conditions, which control the lower tail of the excess loss; and the newly introduced witness condition, which controls the upper tail. The parameter $v$ in the $v$-GRIP conditions determines the achievable rate and is akin to the exponent in the Tsybakov margin condition and the Bernstein condition for bounded losses, which the $v$-GRIP conditions generalize; favorable $v$ in combination with small model complexity leads to $ ilde{O}(1/n)$ rates. The witness condition allows us to connect the excess risk to an 'annealed' version thereof, by which we generalize several previous results connecting Hellinger and Rényi divergence to KL divergence.

We consider the standard model of distributed optimization of a sum of functions $F(mathbf z) = sum_{i=1}^n f_i(mathbf z)$, where node $i$ in a network holds the function $f_i(mathbf z)$. We allow for a harsh network model characterized by asynchronous updates, message delays, unpredictable message losses, and directed communication among nodes. In this setting, we analyze a modification of the Gradient-Push method for distributed optimization, assuming that (i) node $i$ is capable of generating gradients of its function $f_i(mathbf z)$ corrupted by zero-mean bounded-support additive noise at each step, (ii) $F(mathbf z)$ is strongly convex, and (iii) each $f_i(mathbf z)$ has Lipschitz gradients. We show that our proposed method asymptotically performs as well as the best bounds on centralized gradient descent that takes steps in the direction of the sum of the noisy gradients of all the functions $f_1(mathbf z), ldots, f_n(mathbf z)$ at each step.

Tree data are ubiquitous because they model a large variety of situations, e.g., the architecture of plants, the secondary structure of RNA, or the hierarchy of XML files. Nevertheless, the analysis of these non-Euclidean data is difficult per se. In this paper, we focus on the subtree kernel that is a convolution kernel for tree data introduced by Vishwanathan and Smola in the early 2000's. More precisely, we investigate the influence of the weight function from a theoretical perspective and in real data applications. We establish on a 2-classes stochastic model that the performance of the subtree kernel is improved when the weight of leaves vanishes, which motivates the definition of a new weight function, learned from the data and not fixed by the user as usually done. To this end, we define a unified framework for computing the subtree kernel from ordered or unordered trees, that is particularly suitable for tuning parameters. We show through eight real data classification problems the great efficiency of our approach, in particular for small data sets, which also states the high importance of the weight function. Finally, a visualization tool of the significant features is derived.

Israel Martínez-Hernández, Marc G. Genton.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 2, 204--229.

Abstract:
As high-dimensional and high-frequency data are being collected on a large scale, the development of new statistical models is being pushed forward. Functional data analysis provides the required statistical methods to deal with large-scale and complex data by assuming that data are continuous functions, for example, realizations of a continuous process (curves) or continuous random field (surfaces), and that each curve or surface is considered as a single observation. Here, we provide an overview of functional data analysis when data are complex and spatially correlated. We provide definitions and estimators of the first and second moments of the corresponding functional random variable. We present two main approaches: The first assumes that data are realizations of a functional random field, that is, each observation is a curve with a spatial component. We call them spatial functional data . The second approach assumes that data are continuous deterministic fields observed over time. In this case, one observation is a surface or manifold, and we call them surface time series . For these two approaches, we describe software available for the statistical analysis. We also present a data illustration, using a high-resolution wind speed simulated dataset, as an example of the two approaches. The functional data approach offers a new paradigm of data analysis, where the continuous processes or random fields are considered as a single entity. We consider this approach to be very valuable in the context of big data.

Mohd Arshad, Omer Abdalghani.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 167--182.

Abstract:
Suppose that $pi_{1},pi_{2},ldots ,pi_{k}$ be $k(geq2)$ independent exponential populations having unknown location parameters $mu_{1},mu_{2},ldots,mu_{k}$ and known scale parameters $sigma_{1},ldots,sigma_{k}$. Let $mu_{[k]}=max {mu_{1},ldots,mu_{k}}$. For selecting the population associated with $mu_{[k]}$, a class of selection rules (proposed by Arshad and Misra [ Statistical Papers 57 (2016) 605–621]) is considered. We consider the problem of estimating the location parameter $mu_{S}$ of the selected population under the criterion of the LINEX loss function. We consider three natural estimators $delta_{N,1},delta_{N,2}$ and $delta_{N,3}$ of $mu_{S}$, based on the maximum likelihood estimators, uniformly minimum variance unbiased estimator (UMVUE) and minimum risk equivariant estimator (MREE) of $mu_{i}$’s, respectively. The uniformly minimum risk unbiased estimator (UMRUE) and the generalized Bayes estimator of $mu_{S}$ are derived. Under the LINEX loss function, a general result for improving a location-equivariant estimator of $mu_{S}$ is derived. Using this result, estimator better than the natural estimator $delta_{N,1}$ is obtained. We also shown that the estimator $delta_{N,1}$ is dominated by the natural estimator $delta_{N,3}$. Finally, we perform a simulation study to evaluate and compare risk functions among various competing estimators of $mu_{S}$.

Ahmad Younso.

Source: Brazilian Journal of Probability and Statistics, Volume 34, Number 1, 112--126.

Abstract:
We consider a new nonparametric rule of classification, inspired from the classical moving window rule, that allows for the classification of spatially dependent functional data containing some completely missing curves. We investigate the consistency of this classifier under mild conditions. The practical use of the classifier will be illustrated through simulation studies.

Abbas Pak, M. E. Ghitany, Mohammad Reza Mahmoudi.

Source: Brazilian Journal of Probability and Statistics, Volume 33, Number 4, 894--914.

Abstract:
This paper focuses on Bayesian estimation of the parameters and reliability function of the power Lindley distribution by using various symmetric and asymmetric loss functions. Assuming suitable priors on the parameters, Bayes estimates are derived by using squared error, linear exponential (linex) and general entropy loss functions. Since, under these loss functions, Bayes estimates of the parameters do not have closed forms we use lindley’s approximation technique to calculate the Bayes estimates. Moreover, we obtain the Bayes estimates of the parameters using a Markov Chain Monte Carlo (MCMC) method. Simulation studies are conducted in order to evaluate the performances of the proposed estimators under the considered loss functions. Finally, analysis of a real data set is presented for illustrative purposes.

Umberto Amato, Anestis Antoniadis, Italia De Feis.

Source: Statistics Surveys, Volume 14, 32--70.

Abstract:
We present and compare some nonparametric estimation methods (wavelet and/or spline-based) designed to recover a one-dimensional piecewise-smooth regression function in both a fixed equidistant or not equidistant design regression model and a random design model. Wavelet methods are known to be very competitive in terms of denoising and compression, due to the simultaneous localization property of a function in time and frequency. However, boundary assumptions, such as periodicity or symmetry, generate bias and artificial wiggles which degrade overall accuracy. Simple methods have been proposed in the literature for reducing the bias at the boundaries. We introduce new ones based on adaptive combinations of two estimators. The underlying idea is to combine a highly accurate method for non-regular functions, e.g., wavelets, with one well behaved at boundaries, e.g., Splines or Local Polynomial. We provide some asymptotic optimal results supporting our approach. All the methods can handle data with a random design. We also sketch some generalization to the multidimensional setting. To study the performance of the proposed approaches we have conducted an extensive set of simulations on synthetic data. An interesting regression analysis of two real data applications using these procedures unambiguously demonstrates their effectiveness.