Nonparametric Regression with Rescaled Autoregressive Errors

• Activity Number: 613
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Michael Levine*+ and Jose E. Figueroa-Lopez
• Companies: Purdue University and Department of Statistics Purdue University
• Keywords: autoregressive error process ; heteroscedastic ; semiparametric estimators ; difference based estimation approach

Abstract

Nonparametric regression models often have a non-trivial error covariance structure that can be modeled by viewing errors as a time series process. The knowledge of the covariance structure is needed when estimating the variance of regression function estimators or when using bootstrap methods to construct confidence bands for the regression mean.

In our work, we consider a heteroscedastic nonparametric regression model with an autoregressive error process of finite known order p. The heteroscedasticity is incorporated using a scaling function that is defined at uniformly spaced design points on a finite closed interval. We provide an innovative nonparametric estimator of the variance function and establish its consistency and asymptotic normality. We also propose a semiparametric estimator for the vector of autoregressive error process coefficients that is consistent at the square root of the sample size rate and asymptotically normal. Explicit asymptotic covariance matrix is obtained as well. The finite sample performance of the proposed method is tested in simulations and a real data application is provided.