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 ...

We propose a new robust estimator of the regression coefficients in a linear regression model. The proposed estimator is the only robust estimator based on integration rather than optimization. It allows for dependence between errors and regressors, is √ n–consistent, and asymptotically normal. It moreover has the best– achievable breakdown point of regression–invariant estimators, has bounded ...

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...

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...

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...

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...