A class of local likelihood methods and near-parametric asymptotics

Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 1998 · Volume 60 · Issue 4

Abstract

The local maximum likelihood estimateθ^tof a parameter in a statistical modelf(x, θ) is defined by maximizing a weighted version of the likelihood function which gives more weight to observations in the neighbourhood oft. The paper studies the sense in whichf(t, θ^t) is closer to the true distributiong(t) than the usual estimatef(t, θ^) is. Asymptotic results are presented for the case in which the model misspecification becomes vanishingly small as the sample size tends to ∞. In this setting, the relative entropy risk of the local method is better than that of maximum likelihood. The form of optimum weights for the local likelihood is obtained and illustrated for the normal distribution.

Keywords

Density estimation, Local likelihood, Semiparametric inference

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