Shurong Zheng, Zhao Chen, Hengjian Cui, Runze Li.

Source: The Annals of Statistics, Volume 47, Number 6, 3300--3334.

Abstract:
This paper is concerned with test of significance on high-dimensional covariance structures, and aims to develop a unified framework for testing commonly used linear covariance structures. We first construct a consistent estimator for parameters involved in the linear covariance structure, and then develop two tests for the linear covariance structures based on entropy loss and quadratic loss used for covariance matrix estimation. To study the asymptotic properties of the proposed tests, we study related high-dimensional random matrix theory, and establish several highly useful asymptotic results. With the aid of these asymptotic results, we derive the limiting distributions of these two tests under the null and alternative hypotheses. We further show that the quadratic loss based test is asymptotically unbiased. We conduct Monte Carlo simulation study to examine the finite sample performance of the two tests. Our simulation results show that the limiting null distributions approximate their null distributions quite well, and the corresponding asymptotic critical values keep Type I error rate very well. Our numerical comparison implies that the proposed tests outperform existing ones in terms of controlling Type I error rate and power. Our simulation indicates that the test based on quadratic loss seems to have better power than the test based on entropy loss.

Heng Lian, Kaifeng Zhao, Shaogao Lv.

Source: The Annals of Statistics, Volume 47, Number 5, 2922--2949.

Abstract:
In this paper, we consider the local asymptotics of the nonparametric function in a partially linear model, within the framework of the divide-and-conquer estimation. Unlike the fixed-dimensional setting in which the parametric part does not affect the nonparametric part, the high-dimensional setting makes the issue more complicated. In particular, when a sparsity-inducing penalty such as lasso is used to make the estimation of the linear part feasible, the bias introduced will propagate to the nonparametric part. We propose a novel approach for estimation of the nonparametric function and establish the local asymptotics of the estimator. The result is useful for massive data with possibly different linear coefficients in each subpopulation but common nonparametric function. Some numerical illustrations are also presented.

Chengchun Shi, Rui Song, Zhao Chen, Runze Li.

Source: The Annals of Statistics, Volume 47, Number 5, 2671--2703.

Abstract:
This paper is concerned with testing linear hypotheses in high dimensional generalized linear models. To deal with linear hypotheses, we first propose the constrained partial regularization method and study its statistical properties. We further introduce an algorithm for solving regularization problems with folded-concave penalty functions and linear constraints. To test linear hypotheses, we propose a partial penalized likelihood ratio test, a partial penalized score test and a partial penalized Wald test. We show that the limiting null distributions of these three test statistics are $chi^{2}$ distribution with the same degrees of freedom, and under local alternatives, they asymptotically follow noncentral $chi^{2}$ distributions with the same degrees of freedom and noncentral parameter, provided the number of parameters involved in the test hypothesis grows to $infty$ at a certain rate. Simulation studies are conducted to examine the finite sample performance of the proposed tests. Empirical analysis of a real data example is used to illustrate the proposed testing procedures.

Medha Uppala, Mark S. Handcock.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 339--356.

Abstract:
This paper focuses on spatial and temporal modeling of point processes on linear networks. Point processes on linear networks can simply be defined as point events occurring on or near line segment network structures embedded in a certain space. A separable modeling framework is introduced that posits separate formation and dissolution models of point processes on linear networks over time. While the model was inspired by spider web building activity in brick mortar lines, the focus is on modeling wildfire ignition origins near road networks over a span of 14 years. As most wildfires in California have human-related origins, modeling the origin locations with respect to the road network provides insight into how human, vehicular and structural densities affect ignition occurrence. Model results show that roads that traverse different types of regions such as residential, interface and wildland regions have higher ignition intensities compared to roads that only exist in each of the mentioned region types.

Jared D. Fisher, Davide Pettenuzzo, Carlos M. Carvalho.

Source: The Annals of Applied Statistics, Volume 14, Number 1, 299--338.

Abstract:
We introduce a fast, closed-form, simulation-free method to model and forecast multiple asset returns and employ it to investigate the optimal ensemble of features to include when jointly predicting monthly stock and bond excess returns. Our approach builds on the Bayesian dynamic linear models of West and Harrison ( Bayesian Forecasting and Dynamic Models (1997) Springer), and it can objectively determine, through a fully automated procedure, both the optimal set of regressors to include in the predictive system and the degree to which the model coefficients, volatilities and covariances should vary over time. When applied to a portfolio of five stock and bond returns, we find that our method leads to large forecast gains, both in statistical and economic terms. In particular, we find that relative to a standard no-predictability benchmark, the optimal combination of predictors, stochastic volatility and time-varying covariances increases the annualized certainty equivalent returns of a leverage-constrained power utility investor by more than 500 basis points.

Hongbin Zhang, Lang Wu.

Source: The Annals of Applied Statistics, Volume 13, Number 4, 2140--2157.

Abstract:
For a time-to-event outcome with censored time-varying covariates, a joint Cox model with a linear mixed effects model is the standard modeling approach. In some applications such as AIDS studies, mechanistic nonlinear models are available for some covariate process such as viral load during anti-HIV treatments, derived from the underlying data-generation mechanisms and disease progression. Such a mechanistic nonlinear covariate model may provide better-predicted values when the covariates are left censored or mismeasured. When the focus is on the impact of the time-varying covariate process on the survival outcome, an accelerated failure time (AFT) model provides an excellent alternative to the Cox proportional hazard model since an AFT model is formulated to allow the influence of the outcome by the entire covariate process. In this article, we consider a nonlinear mixed effects model for the censored covariates in an AFT model, implemented using a Monte Carlo EM algorithm, under the framework of a joint model for simultaneous inference. We apply the joint model to an HIV/AIDS data to gain insights for assessing the association between viral load and immunological restoration during antiretroviral therapy. Simulation is conducted to compare model performance when the covariate model and the survival model are misspecified.

Bo Ning, Seonghyun Jeong, Subhashis Ghosal.

Source: Bernoulli, Volume 26, Number 3, 2353--2382.

Abstract:
We study frequentist properties of a Bayesian high-dimensional multivariate linear regression model with correlated responses. The predictors are separated into many groups and the group structure is pre-determined. Two features of the model are unique: (i) group sparsity is imposed on the predictors; (ii) the covariance matrix is unknown and its dimensions can also be high. We choose a product of independent spike-and-slab priors on the regression coefficients and a new prior on the covariance matrix based on its eigendecomposition. Each spike-and-slab prior is a mixture of a point mass at zero and a multivariate density involving the $ell_{2,1}$-norm. We first obtain the posterior contraction rate, the bounds on the effective dimension of the model with high posterior probabilities. We then show that the multivariate regression coefficients can be recovered under certain compatibility conditions. Finally, we quantify the uncertainty for the regression coefficients with frequentist validity through a Bernstein–von Mises type theorem. The result leads to selection consistency for the Bayesian method. We derive the posterior contraction rate using the general theory by constructing a suitable test from the first principle using moment bounds for certain likelihood ratios. This leads to posterior concentration around the truth with respect to the average Rényi divergence of order $1/2$. This technique of obtaining the required tests for posterior contraction rate could be useful in many other problems.

Binyan Jiang, Ziqi Chen, Chenlei Leng.

Source: Bernoulli, Volume 26, Number 2, 1234--1268.

Abstract:
High-dimensional data that evolve dynamically feature predominantly in the modern data era. As a partial response to this, recent years have seen increasing emphasis to address the dimensionality challenge. However, the non-static nature of these datasets is largely ignored. This paper addresses both challenges by proposing a novel yet simple dynamic linear programming discriminant (DLPD) rule for binary classification. Different from the usual static linear discriminant analysis, the new method is able to capture the changing distributions of the underlying populations by modeling their means and covariances as smooth functions of covariates of interest. Under an approximate sparse condition, we show that the conditional misclassification rate of the DLPD rule converges to the Bayes risk in probability uniformly over the range of the variables used for modeling the dynamics, when the dimensionality is allowed to grow exponentially with the sample size. The minimax lower bound of the estimation of the Bayes risk is also established, implying that the misclassification rate of our proposed rule is minimax-rate optimal. The promising performance of the DLPD rule is illustrated via extensive simulation studies and the analysis of a breast cancer dataset.

Stepan Mazur, Dmitry Otryakhin, Mark Podolskij.

Source: Bernoulli, Volume 26, Number 1, 226--252.

Abstract:
In this paper, we investigate the parametric inference for the linear fractional stable motion in high and low frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural non-Gaussian analogue of the scaled fractional Brownian motion. It is fully characterised by the scaling parameter $sigma>0$, the self-similarity parameter $Hin(0,1)$ and the stability index $alphain(0,2)$ of the driving stable motion. The parametric estimation of the model is inspired by the limit theory for stationary increments Lévy moving average processes that has been recently studied in ( Ann. Probab. 45 (2017) 4477–4528). More specifically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of $(sigma,alpha,H)$. We present the law of large numbers and some fully feasible weak limit theorems.

Hicks (Family)

The Democracy Fund + UCLA Nationscape Project found some misinformation about the coronavirus is more widespread that you might think.

Cristiano Villa, Jeong Eun Lee.

Source: Bayesian Analysis, Volume 15, Number 2, 533--558.

Abstract:
In this work we propose a novel model prior for variable selection in linear regression. The idea is to determine the prior mass by considering the worth of each of the regression models, given the number of possible covariates under consideration. The worth of a model consists of the information loss and the loss due to model complexity. While the information loss is determined objectively, the loss expression due to model complexity is flexible and, the penalty on model size can be even customized to include some prior knowledge. Some versions of the loss-based prior are proposed and compared empirically. Through simulation studies and real data analyses, we compare the proposed prior to the Scott and Berger prior, for noninformative scenarios, and with the Beta-Binomial prior, for informative scenarios.

Philippe Gagnon, Alain Desgagné, Mylène Bédard.

Source: Bayesian Analysis, Volume 15, Number 2, 389--414.

Abstract:
Linear regression is ubiquitous in statistical analysis. It is well understood that conflicting sources of information may contaminate the inference when the classical normality of errors is assumed. The contamination caused by the light normal tails follows from an undesirable effect: the posterior concentrates in an area in between the different sources with a large enough scaling to incorporate them all. The theory of conflict resolution in Bayesian statistics (O’Hagan and Pericchi (2012)) recommends to address this problem by limiting the impact of outliers to obtain conclusions consistent with the bulk of the data. In this paper, we propose a model with super heavy-tailed errors to achieve this. We prove that it is wholly robust, meaning that the impact of outliers gradually vanishes as they move further and further away from the general trend. The super heavy-tailed density is similar to the normal outside of the tails, which gives rise to an efficient estimation procedure. In addition, estimates are easily computed. This is highlighted via a detailed user guide, where all steps are explained through a simulated case study. The performance is shown using simulation. All required code is given.

Kelly C. M. Gonçalves, Hélio S. Migon, Leonardo S. Bastos.

Source: Bayesian Analysis, Volume 15, Number 2, 335--362.

Abstract:
The paper introduces a new class of models, named dynamic quantile linear models, which combines dynamic linear models with distribution-free quantile regression producing a robust statistical method. Bayesian estimation for the dynamic quantile linear model is performed using an efficient Markov chain Monte Carlo algorithm. The paper also proposes a fast sequential procedure suited for high-dimensional predictive modeling with massive data, where the generating process is changing over time. The proposed model is evaluated using synthetic and well-known time series data. The model is also applied to predict annual incidence of tuberculosis in the state of Rio de Janeiro and compared with global targets set by the World Health Organization.

Fangzheng Xie, Yanxun Xu.

Source: Bayesian Analysis, Volume 15, Number 1, 159--186.

Abstract:
We propose a kernel mixture of polynomials prior for Bayesian nonparametric regression. The regression function is modeled by local averages of polynomials with kernel mixture weights. We obtain the minimax-optimal contraction rate of the full posterior distribution up to a logarithmic factor by estimating metric entropies of certain function classes. Under the assumption that the degree of the polynomials is larger than the unknown smoothness level of the true function, the posterior contraction behavior can adapt to this smoothness level provided an upper bound is known. We also provide a frequentist sieve maximum likelihood estimator with a near-optimal convergence rate. We further investigate the application of the kernel mixture of polynomials to partial linear models and obtain both the near-optimal rate of contraction for the nonparametric component and the Bernstein-von Mises limit (i.e., asymptotic normality) of the parametric component. The proposed method is illustrated with numerical examples and shows superior performance in terms of computational efficiency, accuracy, and uncertainty quantification compared to the local polynomial regression, DiceKriging, and the robust Gaussian stochastic process.

Ioannis Ntzoufras, Claudia Tarantola, Monia Lupparelli.

Source: Bayesian Analysis, Volume 14, Number 3, 797--823.

Abstract:
We introduce a novel Bayesian approach for quantitative learning for graphical log-linear marginal models. These models belong to curved exponential families that are difficult to handle from a Bayesian perspective. The likelihood cannot be analytically expressed as a function of the marginal log-linear interactions, but only in terms of cell counts or probabilities. Posterior distributions cannot be directly obtained, and Markov Chain Monte Carlo (MCMC) methods are needed. Finally, a well-defined model requires parameter values that lead to compatible marginal probabilities. Hence, any MCMC should account for this important restriction. We construct a fully automatic and efficient MCMC strategy for quantitative learning for such models that handles these problems. While the prior is expressed in terms of the marginal log-linear interactions, we build an MCMC algorithm that employs a proposal on the probability parameter space. The corresponding proposal on the marginal log-linear interactions is obtained via parameter transformation. We exploit a conditional conjugate setup to build an efficient proposal on probability parameters. The proposed methodology is illustrated by a simulation study and a real dataset.

Roderick J. Little.

Source: Statistical Science, Volume 34, Number 4, 580--583.

Andreas Buja, Lawrence Brown, Richard Berk, Edward George, Emil Pitkin, Mikhail Traskin, Kai Zhang, Linda Zhao.

Source: Statistical Science, Volume 34, Number 4, 523--544.

Abstract:
In the early 1980s, Halbert White inaugurated a “model-robust” form of statistical inference based on the “sandwich estimator” of standard error. This estimator is known to be “heteroskedasticity-consistent,” but it is less well known to be “nonlinearity-consistent” as well. Nonlinearity, however, raises fundamental issues because in its presence regressors are not ancillary, hence cannot be treated as fixed. The consequences are deep: (1) population slopes need to be reinterpreted as statistical functionals obtained from OLS fits to largely arbitrary joint ${x extrm{-}y}$ distributions; (2) the meaning of slope parameters needs to be rethought; (3) the regressor distribution affects the slope parameters; (4) randomness of the regressors becomes a source of sampling variability in slope estimates of order $1/sqrt{N}$; (5) inference needs to be based on model-robust standard errors, including sandwich estimators or the ${x extrm{-}y}$ bootstrap. In theory, model-robust and model-trusting standard errors can deviate by arbitrary magnitudes either way. In practice, significant deviations between them can be detected with a diagnostic test.

Matteo Carandini
Nov 1, 1997; 17:8621-8644
Articles

Geoffrey M. Boynton
Jul 1, 1996; 16:4207-4221
Articles

British Auxiliary Units were trained to sabotage the enemy in case of German invasion

The burial site, which contains remains from both the Picts and the Norse, is at risk of disappearing due to coastal erosion

"This could be the oldest and longest-lived team ball game in the world," says one archaeologist

Caernarfon, where the discovery was made, was key to Edward I's conquest of the Welsh

The missionary who lived in the house during the mid-1800s delivered vaccinations to locals during a smallpox epidemic

The liquid inside is 3 percent alcohol by volume—and contains 0.13 milligrams of lead per liter

These flying reptiles patrolled the African skies some 100 million years ago

The 18th-century Edinburgh factory once produced a million bottles a week

The Nunavut government says there is no set limit on how much money it is prepared to spend on hotels for residents required to isolate before they return home.

RCMP say they were first called about the fires at 10 p.m. CST on May 7.

The number of people evaluated for signs of stroke at U.S. hospitals has dropped by nearly 40% during the COVID-19 pandemic, according to a study led by researchers from Washington University School of Medicine in St. Louis who analyzed stroke evaluations at more than 800 hospitals across 49 states and the District of Columbia.

Live professional baseball games could be televised in the United States as early next week, with South Korea's Yonhap News Agency reporting Monday that ESPN and the Korea Baseball Organization are nearing an agreement.

A man from Vermilion Bay, Ont., caught and released a fish that he says could have challenged a 70-year-old record for walleye last weekend.

OM partner finds young men on the street and offers them jobs and a place to study the Bible.

Friends Derek and Josiah, who grew up in OM, talk about their most recent adventure: one year producing videos in the Middle East and North Africa.

The B.C. Wildfire Service and the Adams Lake Fire Department are responding to a wildfire burning east of Kamloops in B.C.'s southern Interior.

Bank of Italy Working Papers by Luca Metelli, Filippo Natoli and Luca Rossi

The post Linear Static FEA Productivity with Simulation Professional appeared first on The SOLIDWORKS Blog.

WHAT’S a little distancing between us? Go on, stick your nose closer to the page or screen. Let’s snuggle in a little closer.

Democrat Gavin Newsom, who takes office Jan. 7, plans to expand full-day kindergarten and child-care offerings in the state, according to media reports.

Babies as young as 12 months are exposed to nearly an hour a day of screen time, despite warnings from pediatricians to avoid digital media exposure for children under a year and a half, according to a new analysis.

Watch students in 8th grade teacher Susie Morehead's class deepen their understanding of math principles by working through problems with their peers.

Current human milk fortifiers fail to provide the higher protein intake that is now recommended for feeding human milk–fed infants. There is a desire to avoid the use of powdered products when feeding these infants.

A new ultraconcentrated liquid human milk fortifier that provides more protein than current powdered fortifiers is safe and supports better growth in human milk–fed infants than a powdered fortifier. (Read the full article)

Gaining intravenous access in children can be difficult. Recently, several near-infrared devices have been introduced attempting to support intravenous cannulation by visualizing veins underneath skin. Only one of those devices has been evaluated systemically thus far and results are inconclusive.

Although it was possible to visualize veins with near-infrared in most patients, the VascuLuminator did not improve the success of cannulation. An explanation is that the main problem is probably not localization of the vein but insertion of the cannula. (Read the full article)

Many children with blunt head trauma and isolated skull fractures are admitted to the hospital. Several small studies suggest that children with simple isolated skull fractures are at very low risk of clinical deterioration.

In this large cohort of children with isolated linear skull fractures after minor blunt head trauma, none developed significant intracranial hemorrhages resulting in neurosurgical interventions. These children may be considered for emergency department discharge if neurologically normal. (Read the full article)

At Amazon right now, you can save up to 47 percent on a Samsung Q60 series QLED 4K Ultra HD smart TV with HDR support and Alexa and Google Assistant compatibility.

Vinod K. Bhutani
Jan 1, 1999; 103:6-14
ARTICLES

Source: www.businessinsider.com - Friday, May 08, 2020
Los Angeles' food truck population of over 800 trucks faces a downturn in profits during the coronavirus pandemic, which threatens the livelihood of dozens of vendors. Trucks, many of which are family-owned, are losing up to 60% to 70% of their business. The disintegration of Los Angeles' food truck scene is creating ripple effects as truck owners, employees, and commissaries take financial hits. California recently allowed food trucks to obtain a permit to sell at rest stops, giving vendors the chance to sell to truckers outside the LA proper. Visit Business Insider's homepage for more stories . Los Angeles' food truck scene of over 800 operational trucks is facing a difficult time as business essentially grinds to a halt during the coronavirus pandemic. Food trucks, which are often run as small family businesses, cost on average $29,000 to run in LA, according to a report by the US Chambers of Commerce . But as the lifeblood of food trucks — foot traffic, social gathering, and events — disappears in the wake of the coronavirus, families and small businesses are suffering. "Food trucks rely on people to gather. That model went away pretty quickly," Ross Resnick, founder of food-truck-booking company Roaming Hunger, told the Orange County Register in March. "Pre-corona, it's events, it's workplaces, it's nighttime gatherings in markets. When you close your eyes and imagine a food truck, you imagine a group of people." There are

By Sr. Joan L. Roccasalvo, C.S.J.

In this political season—some call it the theater of the absurd—discussions about women presidents evoke strong views.

In the1960s, there was one woman whose contributions to society were so far reaching that, if the times had been more propitious to women, she could have been elected President of the United States.  But it was not to be.

Eunice Kennedy (1921-2009)

Eunice was the fifth child and the third daughter born to Rose and Joseph P. Kennedy. As the granddaughter of John F., “Honey Fitz,” Fitzgerald, the famous mayor of Boston, she inherited her mother’s natural political instincts; from her father, the energy, initiative and drive of a human dynamo.    

Rosemary was the third child and first daughter born into the Kennedy family.  Unlike the bright brood of eight other brothers and sisters, she was found to be retarded. Eventually, this fact changed the lives of millions of retarded children and adults because Eunice looked after her older sister for the rest of her life.   

“I had enormous respect for Rosie,” Eunice said of her sister. “If I had never met Rosemary, never known anything about handicapped children, how would I have ever found out?  Nobody accepted them any place.” Through Rosemary’s limitations, Eunice discovered her ministry—really her genius—to spend herself and achieve marvelous things for retarded children throughout the world.  

Academic and Professional Preparation

Educated at the Convent of the Sacred Heart, Roehampton, London and at the Manhattanville College of the Sacred Heart, Eunice graduated from Stanford University in 1943 with a Bachelor’s degree in sociology.  She worked for the Special War Problems Division of the U.S. State Department and eventually moved to the U.S. Justice Department as executive secretary for a project dealing with juvenile delinquency.  

In 1951, she served as a social worker at the Federal Industrial Institution for Women before moving to Chicago to work with the House of the Good Shepherd women’s shelter and the Chicago Juvenile Court.  

In 1953, she married Sargent Shriver, an attorney who later worked in the Kennedy and Johnson administrations.  He was the driving force behind the creation of the Peace Corps; the founder of the Job Corps, and the architect of Johnson’s “war on poverty.”  During his service as the U.S. ambassador to France from 1968 to 1970, Eunice studied intellectual disabilities there.  
    
Advocate for the Mentally Retarded

Among advocates of every kind, Eunice excelled as this country’s advocate for the mentally retarded.   In 1962, an exhausted and distressed mother of a retarded child phoned Eunice at her home.  No summer camp would accept her child, she said. Eunice responded with largesse by opening her own home as a summer camp—free of charge—at Timberlawn, the family estate in Maryland,. She would get in the pool and teach the youngsters to swim, loving them as her own children.

Eunice and Her Brothers

Eunice’s advocacy for the mentally retarded was overshadowed by the political pursuits of her three brothers, but she far surpassed them as the natural politician.  More than once it has been said that Eunice would have made a fine President of the Unites States.

Eunice made it a habit of calling the offices of her more famous brothers urging them to another project for the retarded. Teasingly, they dubbed her repeated requests nagging. Yet, they dared not ignore them.

President Kennedy set up research centers on mental retardation.  Robert Kennedy inspected squalid state mental institutions, and Sen. Edward Kennedy helped write the Americans with Disabilities Act.  “It was extraordinary of her to conceive that she too, could play a role comparable to that of her brothers,” Edward Shorter says, author of The Kennedy Family and the Story of Mental Retardation.  “Her leadership role would be in the area of mental retardation rather than on the big political stage.”

In 1968, Eunice founded the Special Olympics.  Today, they include more than 2.25 million people in 160 countries. “She had the genius to see that she, in fact, was capable of major achievements helping these kids, and that is what she did.  She dedicated her life to it,” writes Shorter.  

Awards

Among the many awards Eunice Kennedy Shriver received, the most notable are:
1984  Presidential Medal of Honor by Ronald Reagan highest civilian award in U.S.
1990  Eagle award from the U.S. Sports Academy
1992  Award for Greatest Public Service Benefiting the Disadvantaged
1995  Second American to appear on a U.S. coin while still living
2006  Papal Knighthood and made Dame of the Order of St. Gregory
2009 Smithsonian Institute’s National Portrait Gallery unveiled an historic portrait of her, the first portrait of the NPG has ever commissioned of an individual who had not served as a US President or First Lady.
2010 The State University of New York at Brockport, home of the 1979 Special Olympics, renamed its football stadium after Eunice Shriver.  (Awarded posthumously)

Later Years    

At 85, Eunice was not about to retire or relax.  She continued her tireless work on the issues concerning those with special needs “because in so many countries, the retarded are not accepted in the schools, not accepted in play programs, just not accepted. We have so much to do.”     Eunice Kennedy Shriver and her husband were devout Roman Catholics and lifelong Democrats. Both staunchly pro-life, Eunice was a member of Feminists for Life. She died in 2009, her husband, in 2011.  

The epilogue of the Book of Proverbs is a fitting tribute to Eunice Kennedy Shriver, a woman of noble character.  She lived for others.

Proverbs 31:10-31 Epilogue: The Wife of Noble Character    
10 [a]A wife of noble character who can find?
    She is worth far more than rubies.
11 Her husband has full confidence in her
    and lacks nothing of value.
12 She brings him good, not harm,
    all the days of her life.
13 She selects wool and flax
    and works with eager hands.
14 She is like the merchant ships,
    bringing her food from afar.
15 She gets up while it is still night;
    she provides food for her family
    and portions for her female servants.
16 She considers a field and buys it;
    out of her earnings she plants a vineyard.
17 She sets about her work vigorously;
    her arms are strong for her tasks.
18 She sees that her trading is profitable,
    and her lamp does not go out at night.
19 In her hand she holds the distaff
    and grasps the spindle with her fingers.
20 She opens her arms to the poor
    and extends her hands to the needy.
21 When it snows, she has no fear for her household;
    for all of them are clothed in scarlet.
22 She makes coverings for her bed;
    she is clothed in fine linen and purple.
23 Her husband is respected at the city gate,
    where he takes his seat among the elders of the land.
24 She makes linen garments and sells them,
    and supplies the merchants with sashes.
25 She is clothed with strength and dignity;
    she can laugh at the days to come.
26 She speaks with wisdom,
    and faithful instruction is on her tongue.
27 She watches over the affairs of her household
    and does not eat the bread of idleness.
28 Her children arise and call her blessed;
    her husband also, and he praises her:
29 “Many women do noble things,
    but you surpass them all.”
30 Charm is deceptive, and beauty is fleeting;
    but a woman who fears the Lord is to be praised.
31 Honor her for all that her hands have done,
    and let her works bring her praise at the city gate.

 

More than 9.3 million U.S. students attended a rural school last year. A new report examines factors that affect them like poverty, academic achievement, and diversity.