JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (07): 69-74.doi: 10.6040/j.issn.1671-9352.0.2014.139

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Restricted statistical inference for partially linear models with error-prone covariates

ZHAO Pei-xin1, ZHOU Xiao-shuang2   

  1. 1. College of Mathematics and Statistics, Hechi University, Yizhou 546300, Guangxi, China;
    2. College of Mathematics Sciences, Dezhou University, Dezhou 253000, Shandong, China
  • Received:2014-04-08 Online:2014-07-20 Published:2014-09-15

Abstract: The statistical inference for the partially linear models with error-prone covariates were considered. A restricted least square estimation procedure of parametric components was proposed, and the resulting estimator was shown to be asymptotic normality. Moreover, a Lagrange multiplier testing method was proposed to test the validity of the linear restriction. It was proved that the proposed testing statistic follows an asymptotic standard Chi-square distribution under the null hypothesis. Simulation studies imply that the proposed estimation procedure can attenuate the effect of measurement errors, and the proposed testing method is more powerful.

Key words: error-prone covariates, restricted estimator, partially linear models, Lagrange multiplier test

CLC Number: 

  • O212.7
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