Likelihood ratio tests in linear mixed models with one variance component

被引:299
作者
Crainiceanu, CM [1 ]
Ruppert, D [1 ]
机构
[1] Cornell Univ, Dept Stat, Ithaca, NY 14853 USA
关键词
degrees of freedom; non-regular problems; penalized splines;
D O I
10.1111/j.1467-9868.2004.00438.x
中图分类号
O21 [概率论与数理统计]; C8 [统计学];
学科分类号
020208 ; 070103 ; 0714 ;
摘要
We consider the problem of testing null hypotheses that include restrictions on the variance component in a linear mixed model with one variance component and we derive the finite sample and asymptotic distribution of the likelihood ratio test and the restricted likelihood ratio test. The spectral representations of the likelihood ratio test and the restricted likelihood ratio test statistics are used as the basis of efficient simulation algorithms of their null distributions. The large sample chi(2) mixture approximations using the usual asymptotic theory for a null hypothesis on the boundary of the parameter space have been shown to be poor in simulation studies. Our asymptotic calculations explain these empirical results. The theory of Self and Liang applies only to linear mixed models for which the data vector can be partitioned into a large number of independent and identically distributed subvectors. One-way analysis of variance and penalized splines models illustrate the results.
引用
收藏
页码:165 / 185
页数:21
相关论文
共 27 条
[1]   Testing when a parameter is on the boundary of the maintained hypothesis [J].
Andrews, DWK .
ECONOMETRICA, 2001, 69 (03) :683-734
[2]  
[Anonymous], J AM STAT ASSOC
[3]  
AZZALINI A, 1993, J ROY STAT SOC B MET, V55, P549
[4]  
Brumback BA, 1999, J AM STAT ASSOC, V94, P794, DOI 10.2307/2669991
[5]   Degrees-of-freedom tests for smoothing splines [J].
Cantoni, E ;
Hastie, T .
BIOMETRIKA, 2002, 89 (02) :251-263
[6]  
CRAINICEANU CM, 2003, IN PRESS SOME PROPER
[7]  
CRAINICEANU CM, 2003, IN PRESS EXACT LIKEL
[8]  
CRAINICEANU CM, 2003, TR1389 CORNL U DEP S
[9]   STATISTICAL-INFERENCE USING MAXIMUM-LIKELIHOOD-ESTIMATION AND THE GENERALIZED LIKELIHOOD RATIO WHEN THE TRUE PARAMETER IS ON THE BOUNDARY OF THE PARAMETER SPACE [J].
FENG, ZD ;
MCCULLOCH, CE .
STATISTICS & PROBABILITY LETTERS, 1992, 13 (04) :325-332
[10]   SPLINE-BASED TESTS IN SURVIVAL ANALYSIS [J].
GRAY, RJ .
BIOMETRICS, 1994, 50 (03) :640-652