Minimum Hellinger Distance Estimation of a Regression Function in a Parametric Family with a Random Design

• Activity Number: 134
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Hemalika Abeysundara*+ and Frits Ruymgaart
• Companies: and Texas Tech University
• Keywords: Hellinger Distance ; Measurable space ; Parameter estimation ; Regression Function

Abstract

There is a vast number of methods to estimate parameters of a statistical model based on maximizers and minimizers. These methods compete each other based on their properties such as unbiasness, robustness and efficiency. Some parameter estimation methods work best for specific models and fail when the underlying distribution undergoes even a slightest change due to the lack of robustness. Beran proposed an estimator based on Minimum Hellinger Distance (MHD) method that turned out to be both efficient and robust. Here we exploit his idea in the context of regression estimation. We consider a regression problem with random design where the regression function is defined on an arbitrary measurable space and is assumed to belong to a parametric family with parameter is a compact subset of the real line. In this random design model, the design variable is drawn form an unknown, completely arbitrary probability distribution on the design space. The error variable is assumed to have a known density with a finite second moment and zero mean. Moreover, we assume that the design variable and the error variable are stochastically independent. Summarizing, the response variable of the regress