Recursive local polynomial regression under dependence conditions |
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Authors: | Juan M Vilar-Fernández José A Vilar-Fernández |
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Affiliation: | 1. Departmento de Matemáticas, Universidade de A Coru?a, 15071, A Coru?a, Spain
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Abstract: | In the case of the random design nonparametric regression, one recursive local polynomial smoother is considered. Expressions
for the bias and the variance matrix of the estimators of the regression function and its derivatives are obtained under dependence
conditions (strongly mixing processes). The obtained Mean Squared Error is shown to be larger than those of the analogous
nonrecursive regression estimators, although retaining the same convergence rate. The properties of strong consistency with
convergence rates are established for the proposed estimators. Finally, in order to analyse the influence of both the sample
size and the dependence in the behaviour of the proposed recursive estimator, a simulation study is performed.
This work has been partially supported by DGES Grant PB98-0182-C02-01 and by the Xunta de Galicia Grant XUGA10501B97 |
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Keywords: | Local polynomial fitting recursive nonparametric estimation strongly mixing processes |
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