Asymptotic optimality of the Bayes estimator on Differentiable in Quadratic Mean models

Roudolf Iasnogorodski (1) , Hugo Lhéritier (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

This paper deals with the study of the Bayes estimator's asymptotic properties on Differentiable in Quadratic Mean (DQM) models in the case of independent and identically distributed observations. The investigation is led in order to define weak assumptions on the model under which this estimator is asymptotically efficient, regular and asymptotically of minimal risk. The results of the paper are applied to models based on a mixture distribution, the Cauchy with location and scale parameter's and the Weibull's

Keywords: Parameter estimation; Bayes estimator; DQM models; Asymptotic efficiency; Regular estimator; Asymptotic risk

Domains: Statistics [math.ST]

Roudolf Iasnogorodski, Hugo Lhéritier. Asymptotic optimality of the Bayes estimator on Differentiable in Quadratic Mean models. Proceedings of the SPb department of the Steklov Mathematical Institute, 2005, 328, Probability and Statistics 9, pp. : 114-146. ⟨hal-00023210⟩