On the Preliminary Test Backfitting and Speckman Estimators in Partially Linear Models and Numerical Comparisons

Abstract

Przystalski and Krajewski (2007) 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.

Keywords:

• Backfitting estimator
• Partially linear model
• Preliminary test
• Simulation
• Speckman estimator

Mathematics Subject Classification:

• Primary 62G08
• 62F03

Acknowledgments

The authors are very grateful to the two anonymous referees for their helpful suggestions which improved the presentation of the paper. This research was supported by the National Natural Science Foundation of China (No. 11001286).