Model checking for partially linear models with missing responses at random

Authors:
Zhihua Sun;Qihua Wang;Pengjie Dai
Affiliations:
Department of Mathematics, Graduate University of Chinese Academy of Sciences, Beijing 100049, China and Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, Ch ...;Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China and Department of Statistics & Actuarial Science, The University of Hong Kong, Pokfulam Road, Hong Ko ...;Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100080, China
Venue:
Journal of Multivariate Analysis
Year:
2009

Citing 3
Cited 0

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Abstract

In this paper, we investigate the model checking problem for a partial linear model while some responses are missing at random. By imputation and marginal inverse probability weighted methods, two completed data sets are constructed. Based on the two completed data sets, we build two empirical process-based tests for examining the adequacy of partial linearity of the model. The asymptotic distributions of the test statistics under the null hypothesis and local alternative hypotheses are obtained respectively. A re-sampling approach is applied to obtain the approximation to the null distributions of the test statistics. Simulation results show that the proposed tests work well and both proposed methods have better finite sample properties compared with the complete case (CC) analysis which discards all the subjects with missing data.