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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/192

Title: Efficiency of linear regression estimators based on presmoothing
Authors: JANSSEN, Paul
Keywords: Mathematical Statistics
Non and semiparametric methods
Issue Date: 2001
Citation: Communications in Statistics A, 30(10). p. 2079-2097
Abstract: Consider the estimation of the regression parameters in the usual linear model. For design densities with infinite support, it has been shown by Faraldo Foca and González Manteiga(1) that it is possible to modify the classical least squares procedures and to obtain estimators for the regression parameters whose MSE's(mean squared errors) are smaller than those of the usual least squared estimators. The modification consists of presmoothing the response variables by a kernel estimator of the regression function. These authors also show that the gain in efficiency is not possible for a design density with compact support. We show that in this case local linear fitting automatically corrects the bias in the endpoints of the (design density) support. We demonstrate on a theoretical basis how this inefficiency problem can be rectified in the compact design case: we prove that presmoothing with boundary kernels studied in Müller(2) and Müler and Wang(3) leads to regression estimators which are superior over the least squares estimators. A very careful analytic treatment is needed to arrive at these asymptotic results.
URI: http://hdl.handle.net/1942/192
DOI: 10.1081/STA-100106064
ISI #: 000171406600008
ISSN: 0361-0926
Category: A1
Type: Journal Contribution
Validation: ecoom, 2002
Appears in Collections: Research publications

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