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Restricted likelihood ratio lack‐of‐fit tests using mixed spline models
Author(s) -
Claeskens Gerda
Publication year - 2004
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/j.1467-9868.2004.05421.x
Subject(s) - mathematics , statistics , likelihood ratio test , variance function , statistic , regression analysis , spline (mechanical) , likelihood function , restricted maximum likelihood , estimation theory , structural engineering , engineering
Summary. Penalized regression spline models afford a simple mixed model representation in which variance components control the degree of non‐linearity in the smooth function estimates. This motivates the study of lack‐of‐fit tests based on the restricted maximum likelihood ratio statistic which tests whether variance components are 0 against the alternative of taking on positive values. For this one‐sided testing problem a further complication is that the variance component belongs to the boundary of the parameter space under the null hypothesis. Conditions are obtained on the design of the regression spline models under which asymptotic distribution theory applies, and finite sample approximations to the asymptotic distribution are provided. Test statistics are studied for simple as well as multiple‐regression models.