In the presence of prior information on an unknown parameter of a statistical model, Bayesian and frequentist estimates based on the same observed data do not coincide. However, in many standard parametric problems, this difference tends to decrease for growing sample size. In this paper we consider as a measure of discrepancy (D) the squared difference between Bayesian and frequentist point estimators of the parameter of a model. We derive the predictive distribution of D, for finite sample sizes in the case of a one-dimensional exponential family and we study its behavior for increasing sample size. Numerical examples are illustrated for normal models. (C) 2013 Elsevier B.V. All rights reserved.

Predictive measures of the conflict between frequentist and Bayesian estimators / Brutti, Pierpaolo; DE SANTIS, Fulvio; Gubbiotti, Stefania. - In: JOURNAL OF STATISTICAL PLANNING AND INFERENCE. - ISSN 0378-3758. - STAMPA. - 148:(2014), pp. 111-122. [10.1016/j.jspi.2013.12.009]

Predictive measures of the conflict between frequentist and Bayesian estimators

BRUTTI, Pierpaolo;DE SANTIS, Fulvio;GUBBIOTTI, STEFANIA
2014

Abstract

In the presence of prior information on an unknown parameter of a statistical model, Bayesian and frequentist estimates based on the same observed data do not coincide. However, in many standard parametric problems, this difference tends to decrease for growing sample size. In this paper we consider as a measure of discrepancy (D) the squared difference between Bayesian and frequentist point estimators of the parameter of a model. We derive the predictive distribution of D, for finite sample sizes in the case of a one-dimensional exponential family and we study its behavior for increasing sample size. Numerical examples are illustrated for normal models. (C) 2013 Elsevier B.V. All rights reserved.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/539401
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