Highly Efficient Robust Estimation and Inference Based on Focused Information Criterion and Model Averaging

• Activity Number: 28
• Type: Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Ganggang Xu*+ and Suojin Wang and Jianhua Huang
• Companies: Texas A&M University and Texas A&M University and Texas A&M University
• Keywords: Model inference ; Focused information criterion ; Frequentist Model averaging ; $M$-estimator ; Composite $M$-estimator ; Composite $L$-estimator

Abstract

We study the focused information criterion (FIC) and frequentist model averaging (FMA) and their application to post model selection inference for $M$-estimators in the context of the additive partial linear model. With the nonparametric functions approximated by polynomial splines, we show that, under certain conditions, the asymptotic distribution of the FMA $M$-estimator of a focused parameter is a nonlinear mixture of normal distributions. This asymptotic distribution is used to construct confidence intervals that achieve the nominal coverage probability. Furthermore, we propose two FIC-based composite FMA $M$-estimators that are not only robust to outliers and nonnormal residuals but also of efficiency close to the maximum likelihood estimator, without assuming the true error distribution. Simulation studies and a real data analysis are used to illustrate the effectiveness of the proposed procedures.