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Journal of Applied Mathematics and Stochastic Analysis
Volume 15, Issue 3, Pages 207-219
http://dx.doi.org/10.1155/S1048953302000187

Strong Consistency of Estimators for Heteroscedastic Partly Linear Regression Model under Dependent Samples

1Tongji University, Department of Applied Mathematics, Shanghai 200092, China
2Hong Kong University of Science and Technology, Department of Mathematics, Clear Water Bay, Kowloon, Hong Kong

Received 1 July 2001; Revised 1 February 2002

Copyright © 2002 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this paper we are concerned with the heteroscedastic regression model yi=xiβ+g(ti)+σiei,1in under correlated errors ei, where it is assumed that σi2=f(ui), the design points (xi,ti,ui) are known and nonrandom, and g and f are unknown functions. The interest lies in the slope parameter β. Assuming the unobserved disturbance ei are negatively associated, we study the issue of strong consistency for two different slope estimators: the least squares estimator and the weighted least squares estimator.