Density estimation and nonparametric inferences using maximum likelihood weighted kernels

Huang, Alan (2013) Density estimation and nonparametric inferences using maximum likelihood weighted kernels. Journal of Nonparametric Statistics, 25 3: 561-571. doi:10.1080/10485252.2013.797090


Author Huang, Alan
Title Density estimation and nonparametric inferences using maximum likelihood weighted kernels
Journal name Journal of Nonparametric Statistics   Check publisher's open access policy
ISSN 1048-5252
1029-0311
Publication date 2013
Sub-type Article (original research)
DOI 10.1080/10485252.2013.797090
Open Access Status
Volume 25
Issue 3
Start page 561
End page 571
Total pages 11
Place of publication Abingdon, Oxfordshire, United Kingdom
Publisher Taylor & Francis
Collection year 2014
Abstract We show that maximum likelihood weighted kernel density estimation offers a unified approach to density estimation and nonparametric inferences. For density estimation, the approach is a generalisation of the standard kernel density estimator that allows the weights attached to each kernel to be chosen by maximum likelihood, instead of being set to n -1 from the outset (see also Jones, M.C., and Henderson, D.A. (2005), 'Maximum Likelihood Kernel Density Estimation', Technical Report 01/05, Department of Statistics, The Open University, UK). For nonparametric inferences, the approach offers a natural, smoothed analogue to empirical likelihood (Owen, A.B. (2001), Empirical Likelihood, Boca Raton, FL: Chapman and Hall/CRC) for inferences on functionals of the underlying distribution, such as its mean or median. Numerical results demonstrate that the proposed method is comparable to the standard kernel density estimator (of the same bandwidth) for density estimation, but can offer noticeable small-sample improvements over empirical likelihood for inferences when the underlying distribution is continuous.
Keyword Empirical likelihood
Kernel density estimation
Likelihood ratio test
Q-Index Code C1
Q-Index Status Confirmed Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
Non HERDC
 
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Created: Wed, 26 Mar 2014, 13:57:58 EST by Kay Mackie on behalf of Mathematics