Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm
نویسندگان
چکیده
This document contains supplementary material to the paper “Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm”. A description on how to obtain the derivatives of the approximate restricted maximum likelihood (REML) with respect to the variance components is given, as well as the closed-form expressions for maximum likelihood (ML) estimates of the variance components. Furthermore, additional simulation studies are provided.
منابع مشابه
Fast and compact smoothing on large multidimensional grids
A framework of penalized generalized linear models and tensor products of B-splines with roughness penalties allows effective smoothing of data in multidimensional arrays. A straightforward application of the penalized Fisher scoring algorithm quickly runs into storage and computational difficulties. A novel algorithm takes advantage of the special structure of both the data as an array and the...
متن کاملData Driven Adaptive Spline Smoothing
In classical smoothing splines, the smoothness is controlled by a single smoothing parameter that penalizes the roughness uniformly across the whole domain. Adaptive smoothing splines extend this framework to allow the smoothing parameter to change in the domain, adapting to the change of roughness. In this article we propose a data driven method to nonparametrically model the penalty function....
متن کاملMultidimensional P-spline Mixed Models: A unified approach to smoothing on large grids
We consider multidimensional penalized spline mixed models. Currie et al. (2006) emphasized the array nature of the method and Eilers et al. (2006) used multidimensional P -splines together with a new fast and compact algorithm. We combine these ideas and show how to represent multidiensional Psplines as mixed models and propose an atractive unified approach to models which include smooth and r...
متن کاملFast Computation by Subdivision of Multidimensional Splines and Their Applications
We present theory and algorithms for fast explicit computations of uniand multi-dimensional periodic splines of arbitrary order at triadic rational points and of splines of even order at diadic rational points. The algorithms use the forward and the inverse Fast Fourier transform (FFT). The implementation is as fast as FFT computation. The algorithms are based on binary and ternary subdivision ...
متن کاملSmoothing spline Gaussian regression: more scalable computation via efficient approximation
Smoothing splines via the penalized least squares method provide versatile and effective nonparametric models for regression with Gaussian responses. The computation of smoothing splines is generally of the order O.n3/, n being the sample size, which severely limits its practical applicability. We study more scalable computation of smoothing spline regression via certain low dimensional approxi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Statistics and Computing
دوره 25 شماره
صفحات -
تاریخ انتشار 2015