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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 594391, 9 pages
http://dx.doi.org/10.1155/2013/594391
Research Article

Profile Inferences on Restricted Additive Partially Linear EV Models

School of Mathematical Science, Shandong Normal University, Jinan 250014, China

Received 5 June 2013; Revised 1 August 2013; Accepted 7 August 2013

Academic Editor: Qian Guo

Copyright © 2013 Xiuli Wang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the testing problem for the parameter and restricted estimator for the nonparametric component in the additive partially linear errors-in-variables (EV) models under additional restricted condition. We propose a profile Lagrange multiplier test statistic based on modified profile least-squares method and two-stage restricted estimator for the nonparametric component. We derive two important results. One is that, without requiring the undersmoothing of the nonparametric components, the proposed test statistic is proved asymptotically to be a standard chi-square distribution under the null hypothesis and a noncentral chi-square distribution under the alternative hypothesis. These results are the same as the results derived by Wei and Wang (2012) for their adjusted test statistic. But our method does not need an adjustment and is easier to implement especially for the unknown covariance of measurement error. The other is that asymptotic distribution of proposed two-stage restricted estimator of the nonparametric component is asymptotically normal and has an oracle property in the sense that, though the other component is unknown, the estimator performs well as if it was known. Some simulation studies are carried out to illustrate relevant performances with a finite sample. The asymptotic distribution of the restricted corrected-profile least-squares estimator, which has not been considered by Wei and Wang (2012), is also investigated.