Brazilian Journal of Probability and Statistics

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

Zhenghong Wei, Yongbin Fan, and Jun Zhang

Full-text: Open access

Abstract

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.

Article information

Source
Braz. J. Probab. Stat., Volume 30, Number 3 (2016), 464-484.

Dates
Received: February 2014
Accepted: March 2015
First available in Project Euclid: 29 July 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjps/1469807222

Digital Object Identifier
doi:10.1214/15-BJPS289

Mathematical Reviews number (MathSciNet)
MR3531694

Zentralblatt MATH identifier
1381.62233

Keywords
Distortion measurement errors local linear smoothing restricted estimator bootstrap procedure

Citation

Wei, Zhenghong; Fan, Yongbin; Zhang, Jun. Statistical inference on restricted linear regression models with partial distortion measurement errors. Braz. J. Probab. Stat. 30 (2016), no. 3, 464--484. doi:10.1214/15-BJPS289. https://projecteuclid.org/euclid.bjps/1469807222


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