Abstract
In this paper, we consider the goodness-of-fit for checking whether the nonparametric function in a partial linear regression model with missing covariate at random is a parametric one or not. We estimate the selection probability by using parametric and nonparametric approaches. Two score type tests are constructed with the estimated selection probability. The asymptotic distributions of the test statistics are investigated under the null and local alterative hypothesis. Simulation studies are carried out to examine the finite sample performance of the sizes and powers of the tests. We apply the proposed procedure to a data set on the AIDS clinical trial group (ACTG 315) study.
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Acknowledgments
The authors would like to thank two referees for their constructive comments which led to a much improved presentation of the paper. The research was supported by the National Natural Science Foundation of China (No. 11071253) and Beijing Nova Programme (2010B066).
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Xu, W., Guo, X. Checking the adequacy of partial linear models with missing covariates at random. Ann Inst Stat Math 65, 473–490 (2013). https://doi.org/10.1007/s10463-012-0379-4
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DOI: https://doi.org/10.1007/s10463-012-0379-4