Bootstrap Tests for Variance Components in Semiparametric Varying Coefficient Mixed Models

In this paper, we consider bootstrap test methods for variance component in the semiparametric varying coefficient mixed effects model. The score function based methods are commonly used in the hypothesis tests for mixed models, but it needs a larger sample size and the asymptotic quantile of the statistic is sometimes incorrect under finite sample. In this paper, the one sided and two sided bootstrap test methods based on marginal score function are proposed to examine variance components. The test methods are free from the distribution of the random effect, and the nuisance parameters can be estimated under zeros hypotheses, which is different from likelihood based methods. Simulation studies are carried out to compare the empirical level of significance of each test method, and the result suggest the proposed bootstrap methods are practicable for finite samples.