On the Preliminary Test Backfitting and Speckman Estimators in Partially Linear Models and Numerical Comparisons |
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Authors: | Jianwen Xu Hu Yang |
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Affiliation: | 1. Department of Statistics and Actuarial Science , Chongqing University , Chongqing, China xjw@cqu.edu.cn;3. Department of Statistics and Actuarial Science , Chongqing University , Chongqing, China |
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Abstract: | Przystalski and Krajewski (2007 Przystalski , M. , Krajewski , P. ( 2007 ). Constrained estimators of treatment parameters in semiparametric models . Statist. Probab. Lett. 77 : 914 – 919 .[Crossref], [Web of Science ®] , [Google Scholar]) proposed the restricted backfitting (RBCF) estimator and restricted Speckman (RSPC) estimator for the treatment effects in a partially linear model when some additional exact linear restrictions are assumed to hold. In this article, we introduce the preliminary test backfitting (PTBCF) estimator and preliminary test Speckman (PTSPC) estimator when the validity of the restrictions is suspected. Performances of the proposed estimators are examined with respect to the mean squared error (MSE) criterion. In addition, numerical behaviors of the proposed estimators are illustrated and compared via a Monte Carlo simulation study. |
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Keywords: | Backfitting estimator Partially linear model Preliminary test Simulation Speckman estimator |
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