This paper considers simultaneous estimation of multivariate normal mean vector using Zellner's(1994) balanced loss function when 2 is known and unknown. We show that the usual estimator X is minimax and obtain a class of minimax estimators which have uniformly smaller risk than the usual estimator X. Also, we obtain the proper Bayes estimator relative to balanced loss function and nd the minim...

Consider the problem of estimating normal means from independent observations with known variances, possibly different from each other. Suppose that a second-level normal model is specified on the unknown means, with the prior means depending on a vector of covariates and the prior variances constant. For this two-level normal model, existing empirical Bayes methods are constructed from the Bay...

We investigate the asymptotic properties of the maximum likelihhod estimator and Bayes estimator of the drift parameter for stochastic processes satisfying a linear stochastic differential equations driven by fractional Brownian motion. We obtain a Bernstein-von Mises type theorem also for such a class of processes.

This note considers estimation of the mean of a multivariate Gaussian distribution with known variance within the Minimum Message Length (MML) framework. Interestingly, the resulting MML estimator exactly coincides with the positive-part JamesStein estimator under the choice of an uninformative prior. A new approach for estimating parameters and hyperparameters in general hierarchical Bayes mod...

The use of Mathematica in deriving mean likelihood estimators is discussed. Comparisons are made between the mean likelihood estimator, the maximum likelihood estimator, and the Bayes estimator based on a Jeffrey’s noninformative prior. These estimators are compared using the mean-square error criterion and Pitman measure of closeness. In some cases it is possible, using Mathematica, to derive ...

Simultaneous estimation of system and components reliability is considered when independent partition-based Dirichlet(PBD) prior is assigned on components distribution. Denote the lifetime of component j in the i-th system by {Tij , j = 1, 2, 3, . . . ,K} and the end of monitoring time by {τi, i = 1, 2, . . . , n}. Assume that {Tij , i = 1, 2, 3, . . . , n} and {τi, i = 1, 2, . . . , n} are IID...

in this research, an iterative approach is employed to recognize and classify control chart patterns. to do this, by taking new observations on the quality characteristic under consideration, the maximum likelihood estimator of pattern parameters is first obtained and then the probability of each pattern is determined. then using bayes’ rule, probabilities are updated recursively. finally, when...

In a nonlinear regression model with a given prior distribution, the estimator maximizing the posterior probability density is considered (a certain kind of Bayes estimator). It is shown that the prior influences essentially, but in a comprehensive way, the geometry of the model, including the intrinsic curvature measure of nonlinearity which is derived in the paper. The obtained geometrical re...

Of those things that can be estimated well in an inverse problem, which are best to estimate? Backus-Gilbert resolution theory answers a version of this question for linear (or linearized) inverse problems in Hilbert spaces with additive zero-mean errors with known, finite covariance, and no constraints on the unknown other than the data. This paper extends Backus-Gilbert resolution: it defines...

This paper is the second in a series of two on the problem of estimating a function of a probability distribution from a finite set of samples of that distribution. In the first paper1, the Bayes estimator for a function of a probability distribution was introduced, the optimal properties of the Bayes estimator were discussed, and the Bayes and frequency-counts estimators for the Shannon entrop...