Distribution-free lack-of-fit tests in balanced mixed models

作者：Song Weixing^*; Du Juan

来源：Statistics & Probability Letters, 2010, 80(17-18): 1378-1387.

DOI：10.1016/j.spl.2010.05.002

• Mixed model
• Lack-of-fit test
• Khmaladze transformation
• Brownian motion

Here we discuss the problem of fitting a parametric model to the regression function of the fixed effects in a class of balanced mixed effects models. The proposed test is based on the supremum of the Khmaladze transformation of a certain partial sum process of calibrated residuals, and the asymptotic null distribution of this transformed process turns out to be the same as that of a time transformed standard Brownian motion. Moreover, we show that this test is consistent against a large class of fixed alternatives and has non-trivial asymptotic power against a class of nonparametric local alternatives. Simulation studies are conducted to assess the finite sample performance of the proposed test.

• 出版日期2010-9-1