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2008 Case-deletion importance sampling estimators: Central limit theorems and related results
Ilenia Epifani, Steven N. MacEachern, Mario Peruggia
Electron. J. Statist. 2: 774-806 (2008). DOI: 10.1214/08-EJS259

Abstract

Case-deleted analysis is a popular method for evaluating the influence of a subset of cases on inference. The use of Monte Carlo estimation strategies in complicated Bayesian settings leads naturally to the use of importance sampling techniques to assess the divergence between full-data and case-deleted posteriors and to provide estimates under the case-deleted posteriors. However, the dependability of the importance sampling estimators depends critically on the variability of the case-deleted weights. We provide theoretical results concerning the assessment of the dependability of case-deleted importance sampling estimators in several Bayesian models. In particular, these results allow us to establish whether or not the estimators satisfy a central limit theorem. Because the conditions we derive are of a simple analytical nature, the assessment of the dependability of the estimators can be verified routinely before estimation is performed. We illustrate the use of the results in several examples.

Citation

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Ilenia Epifani. Steven N. MacEachern. Mario Peruggia. "Case-deletion importance sampling estimators: Central limit theorems and related results." Electron. J. Statist. 2 774 - 806, 2008. https://doi.org/10.1214/08-EJS259

Information

Published: 2008
First available in Project Euclid: 16 September 2008

zbMATH: 1320.62046
MathSciNet: MR2443196
Digital Object Identifier: 10.1214/08-EJS259

Subjects:
Primary: 62F15 , 62J20

Keywords: infinite variance , influence , leverage , Marginal Residual Sum of Squares , Markov chain Monte Carlo , model averaging , moment index , tail behavior

Rights: Copyright © 2008 The Institute of Mathematical Statistics and the Bernoulli Society

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