We consider estimation of a location vector in the presence of known or unknown scale parameter in three dimensions. The technique of proof is Stein's integration by parts and it is used to cover several cases (e.g., non-unimodal distributions) for which previous results were known only in the...

Let Fn(x) be the empirical distribution function based on n independent random variables X1,...,Xn from a common distribution function F(x), and let be the sample mean. We derive the rate of convergence of to normality (for the regular as well as nonregular cases), a law of iterated logarithm,...

Families of minimax estimators are found for the location parameter of a p-variate (pgt; or = 3) spherically symmetric unimodal(s.s.u.)distribution with respect to general quadratic loss. The estimators of James and Stein, Baranchik, Bock and Strawderman are all considered for this general...

We consider estimation of the mean vector, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$\theta $$</EquationSource> </InlineEquation>, of a spherically symmetric distribution with known scale parameter under quadratic loss and when a residual vector is available. We show minimaxity of generalized Bayes estimators corresponding to superharmonic priors with a non...</equationsource></inlineequation>

For a vast array of general spherically symmetric location-scale models with a residual vector, we consider estimating the (univariate) location parameter when it is lower bounded. We provide conditions for estimators to dominate the benchmark minimax MRE estimator, and thus be minimax under...

Let X ~ N([theta],1), where [theta] [epsilon] [-m, m], for some m 0, and consider the problem of estimating [theta] with quadratic loss. We show that the Bayes estimator [delta]m, corresponding to the uniform prior on [-m, m], dominates [delta]0 (x) = x on [-m, m] and it also dominates the MLE...

This paper is primarily concerned with extending the results of Stein to spherically symmetric distributions. Specifically, when X ∼f(||X - θ||2), we investigate conditions under which estimators of the form X ag(X) dominate X for loss functions ||δ- θ||2 and loss functions which are...

For p 4 and one observation X on a p-dimensional spherically symmetric distribution, minimax estimators of Theta whose risks are smaller than the risk of X (the best invariant estimator) are found when the loss is a nondecreasing concave function of quadratic loss. For n observations X1, X2, ......

This paper presents an expository development of Stein estimation with substantial emphasis of exact results for spherically symmetric distributions. The themes of the paper are: a) that the improvement possible over the best invariant estimator via shrinkage estimation is not surprising but...