Maximizing leave-one-out likelihood for the location parameter of unbounded densities

Krzysztof Podgórski () and Jonas Wallin ()

Annals of the Institute of Statistical Mathematics, 2015, vol. 67, issue 1, 19-38

Abstract: We propose simple estimation of the location parameter for a density that is unbounded at the mode. The estimator maximizes a modified likelihood in which the singular term in the full likelihood is left out, whenever the parameter value approaches a neighborhood of the singularity location. The consistency and super-efficiency of this maximum leave-one-out likelihood estimator is shown through a direct argument. The importance for estimation within parametric families is discussed and illustrated by an example involving the gamma mixture of normal distributions. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Keywords: Unbounded likelihood; Location parameter; Super-efficiency; Generalized asymmetric Laplace distribution (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s10463-013-0437-6

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