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Entropy 2016, 18(7), 273; doi:10.3390/e18070273

Efficiency Bound of Local Z-Estimators on Discrete Sample Spaces

Department of Computer Science and Mathematical Informatics, Nagoya University, Furocho, Chikusaku, Nagoya 464-8603, Japan
Academic Editor: Kevin H. Knuth
Received: 14 June 2016 / Revised: 16 July 2016 / Accepted: 20 July 2016 / Published: 23 July 2016
View Full-Text   |   Download PDF [287 KB, uploaded 23 July 2016]

Abstract

Many statistical models over a discrete sample space often face the computational difficulty of the normalization constant. Because of that, the maximum likelihood estimator does not work. In order to circumvent the computation difficulty, alternative estimators such as pseudo-likelihood and composite likelihood that require only a local computation over the sample space have been proposed. In this paper, we present a theoretical analysis of such localized estimators. The asymptotic variance of localized estimators depends on the neighborhood system on the sample space. We investigate the relation between the neighborhood system and estimation accuracy of localized estimators. Moreover, we derive the efficiency bound. The theoretical results are applied to investigate the statistical properties of existing estimators and some extended ones. View Full-Text
Keywords: Z-estimator; stochastic localization; efficiency; pseudo-likelihood; composite likelihood Z-estimator; stochastic localization; efficiency; pseudo-likelihood; composite likelihood
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Kanamori, T. Efficiency Bound of Local Z-Estimators on Discrete Sample Spaces. Entropy 2016, 18, 273.

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