Statistical inference on restricted partial linear regression models with partial distortion measurement errors

• Published in: Statistica Neerlandica Vol. 70; no. 4; pp. 304 - 331
• Main Authors: Zhang, Jun, Zhou, Nanguang, Sun, Zipeng, Li, Gaorong, Wei, Zhenghong
• Format: Journal Article
• Language: English
• Published: Oxford Blackwell Publishing Ltd 01.11.2016
• Subjects: Asymptotic properties; Bootstrap method; bootstrap procedure; Distortion; distortion measurement errors; Errors; Estimating techniques; Estimators; Hypotheses; Hypothesis testing; Least squares method; local linear smoothing; Mathematical models; Measurement errors; Regression; Regression analysis; restricted estimator; Statistical inference; Statistical tests; Statistics; Studies
• ISSN: 0039-0402; 1467-9574
• DOI: 10.1111/stan.12089

We consider the estimation and hypothesis testing problems for the partial linear regression models when some variables are distorted with errors by some unknown functions of commonly observable confounding variable. 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 under the null hypothesis. 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 analyzed for an illustration.