Bandwidth selection for kernel log-density estimation

Martin L. Hazelton and Murray P. Cox

Computational Statistics & Data Analysis, 2016, vol. 103, issue C, 56-67

Abstract: Kernel estimation of the logarithm of a probability density function at a given evaluation point is studied. The properties of the kernel log-density estimator are heavily influenced by the unboundedness of the log function at zero. In particular, standard asymptotic expansions can provide a poor guide to finite sample behaviour for this estimator, with consequences for the choice of methodology for bandwidth selection. In response, a new approximate cross-validation bandwidth selector is developed. Its theoretical properties are explored and its finite sample behaviour examined in numerical experiments. The proposed methodology is then applied to estimation of log-likelihoods for a complex genetic model used in determining migration rates between village communities on the Indonesian island of Sumba.

Keywords: Approximate likelihood inference; Kernel smoothing; Mean squared error; Simulation; Smooth cross-validation (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:csdana:v:103:y:2016:i:c:p:56-67

DOI: 10.1016/j.csda.2016.05.003

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