STEIN'S METHOD AND THE BERRY-ESSÉEN THEOREM

Stein's method is used to prove the Lindeberg-Feller theorem and a generalization of the Berry-Esséen theorem. The arguments involve only manipulation of probability inequalities, and form an attractive alternative to the less direct Fourier-analytic methods which are traditionally employed.     

Empirical bayes shrinkage estimation of reliability in the exponential distribution

In this paper we propose two empirical Bayes shrinkage estimators for the reliability of the exponential distribution and study their properties. Under the uniform prior distribution and the inverted gamma prior distribution these estimators are developed and compared with a preliminary test estimator and with a shrinkage testimator in terms of mean squared error. The proposed empirical Bayes shrinkage estimator under the inverted gamma prior distribution is shown to be preferable to the preliminary test estimator and the shrinkage testimator when the prior value of mean life is clsoe to the true mean life.     

Risk inflation of sequential tests controlled by alpha investing

Streaming feature selection is a greedy approach to variable selection that evaluates potential explanatory variables sequentially. It selects significant features as soon as they are discovered rather than testing them all and picking the best one. Because it is so greedy, streaming selection can rapidly explore large collections of features. If significance is defined by an alpha investing protocol, then the rate of false discoveries will be controlled. The focus of attention in variable selection, however, should be on fit rather than hypothesis testing. Little is known, however, about the risk of estimators produced by streaming selection and how the configuration of these estimators influences the risk. To meet these needs, we provide a computational framework based on stochastic dynamic programming that allows fast calculation of the minimax risk of a sequential estimator relative to an alternative. The alternative can be data driven or derived from an oracle. This framework allows us to compute and contrast the risk inflation of sequential estimators derived from various alpha investing rules. We find that a universal investing rule performs well over a variety of models and that estimators allowed to have larger than conventional rates of false discoveries produce generally smaller risk.     

LOWER BOUNDS FOR THE NORMAL APPROXIMATION OF A SUM OF INDEPENDENT RANDOM VARIABLES

The rates of convergence to the normal distribution are investigated for a sum of independent random variables. Using Stein's method, we derive a lower bound of the uniform distance between two distributions of independent sum and normal.     

Automatic polynomial wavelet regression

In Oh, Naveau and Lee (2001) a simple method is proposed for reducing the bias at the boundaries for wavelet thresholding regression. The idea is to model the regression function as a sum of wavelet basis functions and a low-order polynomial. The latter is expected to account for the boundary problem. Practical implementation of this method requires the choice of the order of the low-order polynomial, as well as the wavelet thresholding value. This paper proposes two automatic methods for making such choices. Finite sample performances of these two methods are evaluated via numerical experiments.     

On the efficiency of a testimator for the weibull shape parameter

In estimating the shape parameter of a two-parameter Weibull distribution from a failure-censored sample, a recently popular procedure is to employ a testimator which is a shrinkage estimator based on a preliminary hypothesis test for a guessed value of the parameter. Such an adaptive testimator is a linear compound of the guessed value and a statistic. A new compounding coefficient is numerically shown to yield higher efficiency in many situations compared to some of the existing ones.     

Shrinkage Testimators for the Shape Parameter of Pareto Distribution Using LINEX Loss Function

In this article, shrinkage testimators for the shape parameter of a Pareto distribution are considered, when its prior guess value is available. The choices of shrinkage factor are also suggested. The proposed testimators are compared with the minimum risk estimator among the class of unbiased estimators with the LINEX loss function.