splines

The Math Behind Cubic Splines




splines

Understanding splines in the EFFECT statement

This SAS Usage Note illustrates fitting a model containing a spline effect in PROC GLIMMIX. It discusses the spline basis output, the interpretation of the output, how to use the spline model to make predictions, and how to use the LSMEANS and ESTIMATE statements to compute quantities of interest.




splines

Understanding splines in the EFFECT statement

This SAS Usage Note illustrates fitting a model containing a spline effect in PROC GLIMMIX. It discusses the spline basis output, the interpretation of the output, how to use the spline model to make predictions, and how to use the LSMEANS and ESTIMATE statements to compute quantities of interest.




splines

Cutting machine for gears, splines, and other shapes

A cutting machine for gear shaping or the like is provided. The cutting machine includes a gear shaping head. The gear shaping head has a ram that is guided by and reciprocates along a linear guide mounted between a saddle of the gear shaping head and the ram. At least one linear motor reciprocates the ram along a stroke axis relative to the saddle. The ram also carries a rotary drive and a spindle that reciprocate in unison with the ram. The rotary drive directly drives the spindle to journal the spindle through incremental angular positions during gear shaping.




splines

Efficient estimation in single index models through smoothing splines

Arun K. Kuchibhotla, Rohit K. Patra.

Source: Bernoulli, Volume 26, Number 2, 1587--1618.

Abstract:
We consider estimation and inference in a single index regression model with an unknown but smooth link function. In contrast to the standard approach of using kernels or regression splines, we use smoothing splines to estimate the smooth link function. We develop a method to compute the penalized least squares estimators (PLSEs) of the parametric and the nonparametric components given independent and identically distributed (i.i.d.) data. We prove the consistency and find the rates of convergence of the estimators. We establish asymptotic normality under mild assumption and prove asymptotic efficiency of the parametric component under homoscedastic errors. A finite sample simulation corroborates our asymptotic theory. We also analyze a car mileage data set and a Ozone concentration data set. The identifiability and existence of the PLSEs are also investigated.




splines

Approximation and modeling with B-splines / Klaus Höllig, Jörg Hörner

Online Resource