JSM 2005 - Toronto

Abstract #302795

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 229
Type: Contributed
Date/Time: Tuesday, August 9, 2005 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #302795
Title: Nonparametric Regression with Heteroscedastic Long Memory Errors
Author(s): Hongwen Guo*+
Companies: Michigan State University
Address: 810G, Cherry Lane, East Lansing, MI, 48823,
Keywords: Moving average errors ; Local Whittle
Abstract:

This paper considers the estimation of regression and heteroscedasticity functions in nonparametric heteroscedastic regression models with the uniform nonrandom design on the unit interval and long memory moving average errors. The consistency and finite dimensional weak convergence of the regression function estimators are established. The paper also gives the consistency rate of the heteroscedasticity function estimators for all values of the long memory parameter for H between 1/2 and 1, while their asymptotic normality is established only for H between 1/2 and 3/4. Additionally, the local Whittle estimator of H based on the standardized nonparametric residuals is shown to be log (n)-consistent, and the finite dimensional distributions of the studentized versions of the regression function estimators are shown to be asymptotically normal---where n denotes the sample size. These results thus generalize some of the results of Robinson to heteroscedastic regression models with long memory errors.

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