The effect of the regularity of the error process on the performance of kernel regression estimators

This article considers estimation of regression function in the fixed design model , by use of the Gasser and Müller kernel estimator. The point set constitutes the sampling design points, and are correlated errors. The error process is assumed to satisfy certain regularity conditions, namely, it ha...

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Bibliographic Details
Published in:Metrika 2013-08, Vol.76 (6), p.765-781
Main Authors: Benhenni, Karim, Rachdi, Mustapha, Su, Yingcai
Format: Article
Language:English
Subjects:
Economic Theory/Quantitative Economics/Mathematical Methods
Mathematics
Mathematics and Statistics
Probability Theory and Stochastic Processes
Statistics
Statistics Theory
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Summary:This article considers estimation of regression function in the fixed design model , by use of the Gasser and Müller kernel estimator. The point set constitutes the sampling design points, and are correlated errors. The error process is assumed to satisfy certain regularity conditions, namely, it has exactly ( ) quadratic mean derivatives (q.m.d.). The quality of the estimation is measured by the mean squared error (MSE). Here the asymptotic results of the mean squared error are established. We found that the optimal bandwidth depends on the th mixed partial derivatives of the autocovariance function along the diagonal of the unit square. Simulation results for the model of th order integrated Brownian motion error are given in order to assess the effect of the regularity of this error process on the performance of the kernel estimator.
ISSN:0026-1335
1435-926X
DOI:10.1007/s00184-012-0414-8