Premium
Inference in smoothing spline analysis of variance
Author(s) -
Guo Wensheng
Publication year - 2002
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/1467-9868.00367
Subject(s) - smoothing , smoothing spline , inference , mathematics , multivariate statistics , variance function , spline (mechanical) , likelihood function , computer science , mathematical optimization , statistics , algorithm , estimation theory , artificial intelligence , structural engineering , engineering , bilinear interpolation , spline interpolation , linear regression
Summary. Smoothing spline analysis of variance decomposes a multivariate function into additive components. This decomposition not only provides an efficient way to model a multivariate function but also leads to meaningful inference by testing whether a certain component equals 0. No formal procedure is yet available to test such a hypothesis. We propose an asymptotic method based on the likelihood ratio to test whether a functional component is 0. This test allows us to choose an optimal model and to compare groups of curves. We first develop the general theory by exploiting the connection between mixed effects models and smoothing splines. We then apply this to compare two groups of curves and to select an optimal model in a two‐dimensional problem. A small simulation is used to assess the finite sample performance of the likelihood ratio test.