Mathematics – Statistics Theory
Scientific paper
2009-03-03
Annals of Statistics 2009, Vol. 37, No. 1, 427-458
Mathematics
Statistics Theory
Published in at http://dx.doi.org/10.1214/07-AOS561 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Scientific paper
10.1214/07-AOS561
We study semiparametric varying-coefficient partially linear models when some linear covariates are not observed, but ancillary variables are available. Semiparametric profile least-square based estimation procedures are developed for parametric and nonparametric components after we calibrate the error-prone covariates. Asymptotic properties of the proposed estimators are established. We also propose the profile least-square based ratio test and Wald test to identify significant parametric and nonparametric components. To improve accuracy of the proposed tests for small or moderate sample sizes, a wild bootstrap version is also proposed to calculate the critical values. Intensive simulation experiments are conducted to illustrate the proposed approaches.
Liang Hua
Zhou Yong
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