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Robustification Process on Bayes Estimators

Anton Abdulbasah Kamil, (2005) Robustification Process on Bayes Estimators. Matematika, 21 (1). pp. 51-59. ISSN 01278274

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Official URL: http://www.fs.utm.my/matematika/images/stories/matematika/200521105.pdf

Affiliations

Universiti Sains Malaysia, School of Mathematical Sciences

Abstract

The paper describes one possible robustification process on Bayes estimators and studies how a robust estimator can work with prior information. This robustification procedure, as one of possible sensitivity analysis, enables us to study the effect of the outlying observations together with sensitivity to a chosen prior distribution or to a chosen loss function. Consider i.i.d. d-dimensional random vectors X1, ...,Xn with a distribution Pθ depending on an unknown parameter θ Rl. We deal with robust counterparts of maximum posterior likelihood estimators and Bayes estimators in the inference on θ. Asymptotic properties of these robust versions, including their asymptotic equivalence of order op(n−1), are proven.

Item Type:Journal
Keywords:Bayes type estimators, robustification process, asymptotic theory
Subjects:Q Science, Computer Science
ID Code:8800

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[3] N.G. De Bruijn, Asymptotic Methods in Analysis, North-Holland, Amsterdam, 1961.

[4] F.R. Hampel, E.M. Ronchetti, P.J. Rousseeuw and W.A. Stahel, Robust Statistics: The Approach Based on Influence Functions, J. Wiley, New York, 1986.

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[6] H. Strasser, Asymptotic Expansions for Bayes Procedures, In: Recent Development in Statistics (J.R. Barra et al.Ed.), Amsterdam: North-Holland, Amsterdam, 1977, 9-35.

[7] L. Tierney & J Kadane, Accurate Approximations for Posterior Moments and Marginal Densities, JASA, 81(1986), 82-86.

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