A Smooth Simultaneous Confidence Band for Conditional Variance Function

• Activity Number: 74
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Li Cai* and Lijian Yang
• Companies: Soochow University and Soochow University
• Keywords: B spline ; Confidence band ; Heteroscedasticity ; Infeasible estimator ; Nadaraya-Waston estimator ; Variance function

Abstract

A smooth simultaneous confidence band (SCB) is obtained for heteroscedastic variance function in nonparametric regression. The basic idea is to apply spline regression to the conditional mean function followed by Nadaraya-Waston estimation with the squared residuals. The estimator of variance is uniformly oracally efficient, that is, it is as efficient as, up to order smaller than n^{-1/2}, the infeasible kernel estimator when the conditional mean function is known, uniformly over the entire data range. Simulation experiments provide strong evidence that confirms the asymptotic theory while the computing is extremely fast. The proposed SCB has been applied to test for heteroscedasticity in the well-known motorcycle data and Old Faithful geyser data with different conclusions.