文章基本信息

标题：Statistical inference on restricted linear regression models with partial distortion measurement errors
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作者：Zhenghong Wei ; Yongbin Fan ; Jun Zhang 等
期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2016
卷号：30
期号：3
页码：464-484
DOI：10.1214/15-BJPS289
语种：English
出版社：Brazilian Statistical Association
摘要：We consider statistical inference for linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variables. The proposed estimation procedure is designed to accommodate undistorted as well as distorted variables. To test a hypothesis on the parametric components, a restricted least squares estimator is proposed for unknown parameters under some restricted conditions. Asymptotic properties for the estimators are established. A test statistic based on the difference between the residual sums of squares under the null and alternative hypotheses is proposed, and we also obtain the asymptotic properties of the test statistic. A wild bootstrap procedure is proposed to calculate critical values. Simulation studies are conducted to demonstrate the performance of the proposed procedure and a real example is analysed for an illustration.