# Kernel density based linear regression estimate

## K-REx Repository

 dc.contributor.author Yao, Weixin dc.contributor.author Zhao, Zhibiao dc.date.accessioned 2014-03-10T19:58:29Z dc.date.available 2014-03-10T19:58:29Z dc.date.issued 2014-03-10 dc.identifier.uri http://hdl.handle.net/2097/17210 dc.description.abstract For linear regression models with non normally distributed errors, the least squares estimate (LSE) will lose some efficiency compared to the maximum likelihood estimate (MLE). In this article, we propose a kernel density-based regression estimate (KDRE) that is adaptive to the unknown error distribution. The key idea is to approximate the likelihood function by using a nonparametric kernel density estimate of the error density based on some initial parameter estimate. The proposed estimate is shown to be asymptotically as efficient as the oracle MLE which assumes the error density were known. In addition, we propose an EM type algorithm to maximize the estimated likelihood function and show that the KDRE can be considered as an iterated weighted least squares estimate, which provides us some insights on the adaptiveness of KDRE to the unknown error distribution. Our Monte Carlo simulation studies show that, while comparable to the traditional LSE for normal errors, the proposed estimation procedure can have substantial efficiency gain for non normal errors. Moreover, the efficiency gain can be achieved even for a small sample size. en_US dc.language.iso en_US en_US dc.relation.uri http://www.tandfonline.com/doi/full/10.1080/03610926.2011.650269#.UxjwEj9dXL8 en_US dc.rights This is an electronic version of an article published in Communications in Statistics - Theory and Methods, 42(24), 4499-4512. Communications in Statistics - Theory and Methods is available online at: http://www.tandfonline.com/doi/full/10.1080/03610926.2011.650269#.UxjwEj9dXL8 en_US dc.subject EM algorithm en_US dc.subject Kernel density estimate en_US dc.subject Least squares estimate en_US dc.subject Linear regression en_US dc.subject Maximum likelihood estimate en_US dc.title Kernel density based linear regression estimate en_US dc.type Article (author version) en_US dc.date.published 2013 en_US dc.citation.doi doi:10.1080/03610926.2011.650269 en_US dc.citation.epage 4512 en_US dc.citation.issue 24 en_US dc.citation.jtitle Communications in Statistics - Theory and Methods en_US dc.citation.spage 4499 en_US dc.citation.volume 42 en_US dc.contributor.authoreid wxyao en_US
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