Self-Normalized-Based Approach to Nonparametric Inference

• Activity Number: 411
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Zhibiao Zhao and Xiaofeng Shao and Seonjin Kim*+
• Companies: Penn State University and University of Illinois at Urbana-Champaign and Penn State University
• Keywords: Nonparametric regression ; Self-normalization ; Quantile regression ; Conditional heteroscedasticity

Abstract

In nonparametric inference problems, limiting variance function in asymptotic normal distributions often depends on specific model structure and admits a complicated form that may contain unknown nonparametric functions. Traditional approaches construct consistent estimate of the limiting variance function through extra smoothing procedure, which may deliver very unstable results. In this article, we propose self-normalization based approaches to address nonparametric inference problems without estimating the limiting variance functions. It is shown that the new approach has several advantages over the traditional ones. Monte Carlo simulations are conducted to compare the finite sample performance of the self-normalization based approaches with the traditional ones. Illustrations using real data examples are presented.