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Likelihood-based local linear estimation of the conditional variance function

Yu, K. and Jones, M.C. (2004). Likelihood-based local linear estimation of the conditional variance function. Journal of the American Statistical Association, 99(465) pp. 139–144.

DOI (Digital Object Identifier) Link: http://dx.doi.org/10.1198/016214504000000133
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Abstract

We consider estimation of mean and variance functions with kernel-weighted local polynomial fitting in a heteroscedastic nonparametric regression model. Our preferred estimators are based on a localized normal likelihood, using a standard local linear form for estimating the mean and a local log-linear form for estimating the variance. It is important to allow two bandwidths in this problem, separate ones for mean and variance estimation. We provide data-based methods for choosing the bandwidths. We also consider asymptotic results, and study and use them. The methodology is compared with a popular competitor and is seen to perform better for small and moderate sample sizes in simulations. A brief example is provided.

Item Type: Journal Article
ISSN: 1537-274X
Keywords: bandwidth selection; heteroscedasticity; kernel estimation; nonparametric regression
Academic Unit/Department: Mathematics, Computing and Technology > Mathematics and Statistics
Item ID: 2130
Depositing User: M. C. Jones
Date Deposited: 05 Jun 2006
Last Modified: 02 Dec 2010 19:46
URI: http://oro.open.ac.uk/id/eprint/2130
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