TY - JOUR
T1 - Goodness-of-fitting for partial linear model with missing response at random
AU - Xu, Wangli
AU - Guo, Xu
AU - ZHU, Lixing
N1 - Funding Information:
The research was supported by the National Natural Science Foundation of China (No. 11071253), Beijing Nova Programme (2010B066), the Humanities and Social Sciences Project of Chinese Ministry of Education (No. 08JC910002), the MOE Project of Key Research Institute of Humanities and Social Sciences in Universities (No. 2009JJD910002) and a grant from the Research Grant Council of Hong Kong.
PY - 2012/3
Y1 - 2012/3
N2 - In this study, we consider the testing problem about the null hypothesis that the nonlinear part in the partial linear regression model with missing response at random is a parametric function or not against the alternative that it is nonparametric. By imputation and inverse probability weighting methods, we then construct two completed data sets. Two empirical process-based tests, from these completed data sets, are introduced. Under the null hypothesis and local alterative hypotheses, the limiting null distributions and power study of the test statistics are, respectively, investigated. A nonparametric Monte Carlo test procedure, which can automatically make the test procedure scale-invariant even when the test statistics are not scale-invariant, is applied to approximate the limiting null distributions of the test statistics. Simulation study is carried out to examine the performance of the tests. We illustrate the proposed method with a real data set on monozygotic twins.
AB - In this study, we consider the testing problem about the null hypothesis that the nonlinear part in the partial linear regression model with missing response at random is a parametric function or not against the alternative that it is nonparametric. By imputation and inverse probability weighting methods, we then construct two completed data sets. Two empirical process-based tests, from these completed data sets, are introduced. Under the null hypothesis and local alterative hypotheses, the limiting null distributions and power study of the test statistics are, respectively, investigated. A nonparametric Monte Carlo test procedure, which can automatically make the test procedure scale-invariant even when the test statistics are not scale-invariant, is applied to approximate the limiting null distributions of the test statistics. Simulation study is carried out to examine the performance of the tests. We illustrate the proposed method with a real data set on monozygotic twins.
KW - empirical process
KW - goodness-of-fitting
KW - imputation
KW - inverse probability weighting
KW - missing response
UR - http://www.scopus.com/inward/record.url?scp=84863399260&partnerID=8YFLogxK
U2 - 10.1080/10485252.2011.626410
DO - 10.1080/10485252.2011.626410
M3 - Journal article
AN - SCOPUS:84863399260
SN - 1048-5252
VL - 24
SP - 103
EP - 118
JO - Journal of Nonparametric Statistics
JF - Journal of Nonparametric Statistics
IS - 1
ER -