This paper considers the Bayesian point estimation of the scale parameter for a two-parameter gamma life-testl,g model In presence of several outller observations in the data. The Bayesian analysis is carried out under the assumption of squared error loss function and fixed or random shape parameter.

We consider binary classification problems with positive definite kernels and square loss, and study the convergence rates of stochastic gradient methods. We show that while the excess testing loss (squared loss) converges slowly to zero as the number of observations (and thus iterations) goes to infinity, the testing error (classification error) converges exponentially fast if low-noise condit...

The problem of estimating the parameter ?, when it is restricted to an interval of the form , in a class of discrete distributions, including Binomial Negative Binomial discrete Weibull and etc., is considered. We give necessary and sufficient conditions for which the Bayes estimator of with respect to a two points boundary supported prior is minimax under squared log error loss function....

Beamforming methods are used extensively in a variety of different areas, where one of their main goals is to estimate the source signal amplitude s(t) from the array observations y(t) = s(t)a + i(t) + e(t), t = 1,2,..., where a is the steering vector, i(t) is the interference, and e(t) is a Gaussian noise vector [1, 2]. To estimate s(t), we may use a beamformer with weights w so that s(t) = w*...

P erhaps the most surprising result in Statistics arises in a remarkably simple estimation problem. Let X1, ..., Xp be independent random variables, with Xi ∼ N(θi , 1) for i = 1, ..., p. Writing X = (X1, ..., Xp), suppose we want to find a good estimator θ̂ = θ̂(X) of θ = (θ1, ..., θp). To define more precisely what is meant by a good estimator, we use the language of statistical decision theory...

We prove that the standard nonparametric mean estimator for judgment post-stratification is inadmissible under squared error loss within a certain class of linear estimators. We derive alternate estimators that are admissible in this class, and we show that one of them is always better than the standard estimator. The reduction in mean squared error from using this alternate estimator can be as...

The nonparametric problem of estimating a variance based on a sample of size n from a univariate distribution which has a known bounded range but is otherwise arbitrary is treated. For squared error loss, a certain linear function of the sample variance is seen to be minimax for each n from 2 through 13, except n = 4. For squared error loss weighted by the reciprocal of the variance, a constant...

The problem of forming images that are optimal with respect to a Mean Square Error (MSE) criterion, based on nite data, is considered. First, it is shown that the MSE criterion is consistent with the general goal of classifying images, in that decreasing the MSE guarantees a decrease in the probability of misclassifying an image. The problem of choosing sampling locations for image formation th...