Statistical inference on restricted partial linear regression models with partial distortion measurement errors
Corresponding Author
Jun Zhang
College of Mathematics and Statistics, Institute of Statistical Sciences, Shen Zhen-Hong Kong Joint Research Center for Applied Statistical Sciences, Shenzhen University, Shenzhen, 518060 China
Correspondence to:
E-mail: [email protected]
Search for more papers by this authorNanguang Zhou
College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060 China
Search for more papers by this authorZipeng Sun
College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060 China
Search for more papers by this authorGaorong Li
Beijing Center for Scientific and Engineering Computing, College of Applied Sciences, Beijing University of Technology, Beijing, 100124 China
Search for more papers by this authorZhenghong Wei
College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University, Shenzhen, 518060 China
Search for more papers by this authorCorresponding Author
Jun Zhang
College of Mathematics and Statistics, Institute of Statistical Sciences, Shen Zhen-Hong Kong Joint Research Center for Applied Statistical Sciences, Shenzhen University, Shenzhen, 518060 China
Correspondence to:
E-mail: [email protected]
Search for more papers by this authorNanguang Zhou
College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060 China
Search for more papers by this authorZipeng Sun
College of Mathematics and Statistics, Shenzhen University, Shenzhen, 518060 China
Search for more papers by this authorGaorong Li
Beijing Center for Scientific and Engineering Computing, College of Applied Sciences, Beijing University of Technology, Beijing, 100124 China
Search for more papers by this authorZhenghong Wei
College of Mathematics and Statistics, Institute of Statistical Sciences, Shenzhen University, Shenzhen, 518060 China
Search for more papers by this authorAbstract
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.
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