Kernel density based linear regression estimate

K-REx Repository

Show simple item record Yao, Weixin Zhao, Zhibiao 2014-03-10T19:58:29Z 2014-03-10T19:58:29Z 2014-03-10
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 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: 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 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

Files in this item

This item appears in the following Collection(s)

Show simple item record

Search K-REx

Advanced Search


My Account


Center for the

Advancement of Digital