Estimation in partially linear varying-coefficient errors-in-variables models with missing response variables
- PDF / 499,360 Bytes
- 22 Pages / 439.37 x 666.142 pts Page_size
- 94 Downloads / 234 Views
Estimation in partially linear varying-coefficient errors-in-variables models with missing response variables Yan-Ting Xiao1
· Fu-Xiao Li1
Received: 22 February 2018 / Accepted: 5 February 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, a partially linear varying-coefficient model with measurement errors in the nonparametric component as well as missing response variable is studied. Two estimators for the parameter vector and nonparametric function are proposed based on the locally corrected profile least squares method. The first estimator is constructed by using the complete-case data only, and another by using an imputation technique. Both proposed estimators of the parametric component are shown to be asymptotically normal, and the estimators of nonparametric function are proved to achieve the optimal strong convergence rate as the usual nonparametric regression. Some simulation studies are conducted to compare the behavior of these estimators and the results confirm that the estimators based on the imputation technique perform better than the complete-case data estimator in finite samples. Finally, an application to a real data set is illustrated. Keywords Partially linear varying-coefficient models · Measurement error · Missing response · Locally corrected profile least squares · Imputation technique
1 Introduction The partially linear varying-coefficient model, as a very important semi-parametric model, takes the form as Y = XT β + ZT α(U ) + ε,
(1)
where Y is the response variable, X ∈ R p , Z ∈ R q and U are the associated covariates, β = (β1 , . . . , β p )T is a p-dimensional vector of unknown parameter and α(.) = (α1 (.), . . . , αq (.))T is a q-dimensional vector of unknown coefficient function, ε is
B 1
Yan-Ting Xiao [email protected] Department of Applied Mathematics, Xi’an University of Technology, Xi’an 710048, China
123
Y.-T. Xiao, F.-X. Li
the random error that is assumed to be independent of (U , X, Z) with mean zero and finite variance σ 2 . Since model (1) keeps both the interpretation power of parametric model and the flexibility of nonparametric model, it has been extensively studied by researches (Ahmad et al. 2005; Fan and Huang 2005; Kai et al. 2011; Long et al. 2013; You and Zhou 2006; Zhang et al. 2002; among others). With the development of science and technology, the study of data with missing observations has been attracted more attention in various scientific fields, such as economics, engineering, biology and epidemiology. Dealing with missing data, several problems may arise when traditional statistical inference procedures for complete data sets are applied directly. There has been extensive research on statistical models with missing observations. In the partially linear model with the missing response data, Wang et al. (2004) proposed a class of semiparametric estimators for the regression coefficient and the response mean. Wang and Sun (2007) developed the imputation, semi-parametric surrogate regression and inverse mar
Data Loading...
