Robust Difference--Based Estimation in Semiparametric Partially Linear Models

• Activity Number: 238
• Type: Contributed
• Date/Time: Monday, July 30, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Asuman Turkmen*+ and Gulin Tabakan
• Companies: The Ohio State University and Aksaray University
• Keywords: Partially linear models ; Difference based estimation ; Outlier ; Diagnostics ; Robustness

Abstract

Partially linear models are flexible alternatives to the standard linear models, since they combine both parametric and nonparametric components, which may be more adaptive when it is believed that the response depends linearly on some covariates but nonlinearly on others. Therefore, they have received considerable attention in statistics and econometrics literatures during the last three decades. Unfortunately, popular fitting algorithms for these models can be highly sensitive to a small proportion of observations that depart from the model. In this paper, a robust difference based estimator (RDE) is proposed for inference about regression parameters in partially linear models. The classical difference based estimator (CDE) proposed by Yatchew (1997) and the RDE are compared using a real dataset and a simulation study demonstrating that RDE outperforms CDE when the error distribution is not normal, particularly when the errors are heavy-tailed and when outliers are in the dataset. We also represented the results of the robust difference based regression analysis by means of a diagnostic plot by which we can highlight the outliers in the dataset.