The problem considered is sequential estimation of the mean 0 of a one-parameter exponential family of distributions with squared error loss for estimation error and a cost c > 0 for each of an i.i.d, sequence of potential observations X 1, X 2 . . . . . A Bayesian approach is adopted, and natural conjugate prior distributions are assumed. For this problem, the asymptotically pointwise optimal ...

MOTIVATION A major problem of pattern classification is estimation of the Bayes error when only small samples are available. One way to estimate the Bayes error is to design a classifier based on some classification rule applied to sample data, estimate the error of the designed classifier, and then use this estimate as an estimate of the Bayes error. Relative to the Bayes error, the expected e...

We consider the estimation of Markov transition matrices by Bayes’ methods. We obtain large and moderate deviation principles for the sequence of Bayesian posterior distributions. MSC 2000 subject classification: 60F10, 62M05

In this paper, we consider the estimation of the unknown parameter of the scaled logistic distribution on the basis of record values. The maximum likelihood method does not provide an explicit estimator for the scale parameter. In this article, we present a simple method of deriving an explicit estimator by approximating the likelihood function. Bayes estimator is obtained using importance samp...

The use of the Pareto distribution as a model for various socio-economic phenomena dates back to the late nineteenth century. In this paper, after some necessary preliminary results we deal with Bayes estimation of some of the parameters of interest under an asymmetric LINEX loss function, using suitable choice of priors when the scale parameter is known and unknown. Results of a Monte C...