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

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  • Krzysztof Podgórski
  • Jonas Wallin

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

Suggested Citation

  • Krzysztof Podgórski & Jonas Wallin, 2015. "Maximizing leave-one-out likelihood for the location parameter of unbounded densities," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(1), pages 19-38, February.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:1:p:19-38
    DOI: 10.1007/s10463-013-0437-6
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    References listed on IDEAS

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    1. Seo, Byungtae & Kim, Daeyoung, 2012. "Root selection in normal mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2454-2470.
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    Cited by:

    1. Thanakorn Nitithumbundit & Jennifer S. K. Chan, 2020. "ECM Algorithm for Auto-Regressive Multivariate Skewed Variance Gamma Model with Unbounded Density," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1169-1191, September.

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