A formal bayes multiple shrinkage estimator

A new minimax multiple shrinkage estimator is constructed. This estimator which can adaptively shrink towards many subspace targets, is formal Bayes with respect to a mixture of harmonic priors. Unbiased estimates of risk and simulation results suggest that the risk properties of this estimator are very similar to those of the multiple shrinkage Stein estimator proposed by George (1986a). A special case is seen to be admissible.     

Asymptotic test statistics for coefficients of variation

A one-sample asymptotically normal test statistic Is derived for testing the hypothesis that the coefficient of variation of a normal population is equal to a specified value. Based on this derivation, an asymptotically noraml two-sample test statistic and an asymptotically chi-square k-sample test statistic are derived for testing the hypothesis that the coefficients of variation of k ≥2 normal populations are equal. The two and k-sample test statistics allow for unequal sample sizes. Results of a simulation study which evaluate the size and power of the test statistics and compare the test statistics to earlier ones developed by McKay (1932) and Bennett (1976) are presented.     

A transformation for estimating the trinomial logit model with grouped data

For logit models where the outcome variables are the proportions of individuals falling into each of three categories, this paper develops a data transformation through which GLS estimates can be obtained by running OLS on the transformed data.     

Bayesian consistency for regression models under a supremum distance

This paper studies the consistency of Bayesian nonparametric regression models. We concentrate on the use of the sup metric and dealing with non-stochastic, i.e. designed, covariate values. We illustrate our results on a normal mean regression function and demonstrate the usefulness of a model based on piecewise constant functions.     

Estimating the Cost of a Warranty

The cost of certain types of warranties is closely related to functions that arise in renewal theory. The problem of estimating the warranty cost for a random sample of size n can be reduced to estimating these functions. In an earlier paper, I gave several methods of estimating the expected number of renewals, called the renewal function. This answered an important accounting question of how to arrive at a good approximation of the expected warranty cost. In this article, estimation of the renewal function is reviewed and several extensions are given. In particular, a resampling estimator of the renewal function is introduced. Further, I argue that managers may wish to examine other summary measures of the warranty cost, in particular the variability. To estimate this variability, I introduce estimators, both parametric and nonparametric, of the variance associated with the number of renewals. Several numerical examples are provided.     

Comparisons of changepoint estimators

Statistical comparisons of several nonparametric changepoint estimators which are currently offered in the literature are undertaken. The criteria for comparison are Pitman nearness, probability concentration and mean squared error. Recommendations for small, moderate and large sample cases are given.     

An Iterative Weighted Least Squares Algorithm and Simulation Study for Censored Data M-Estimates

A popular linear regression estimator for censored data is the one proposed by Buckley and James (1979). However, this estimator is not robust to outliers, which is not surprising since it is a modified version of the uncensored data least squares estimator. Lai and Ying (1994) have proposed an M-estimator for censored data that is a generalization of the Buckley- James estimator. In this paper we discuss a weighted least squares algorithm for computing these M-estimates and compare the performance of two Huber M-estimators with the Buckley-James estimator in a simulation study. We find that the Huber M-estimators perform more robustly for a broad range of censoring and error distributions.     

Sup–Hellinger consistency for local density regression

Abstract

This article studies the consistency of a local density regression model under a supremum Hellinger distance. Such model applies a piecewise structure where a mixture of Dirichlet process model (MDP) is assigned as the fixed density on each piece. The piecewise construction is a straightforward way to establish sup–Hellinger consistency in a regression settings. A specific piecewise density example is presented in a simulation study.     

Two-step calibration of design weights in survey sampling

ABSTRACT

In this article, a new two-step calibration technique of design weights is proposed. In the first step, the calibration weights are set proportional to the design weights in a given sample. In the second step, the constants of proportionality are determined based on different objectives of the investigator such as bias reduction or minimum mean squared error. Many estimators available in the literature can be shown to be special cases of the proposed two-step calibrated estimator. A simulation study, based on a real data set, is also included at the end. A few technical issues are raised with respect to the use of the proposed calibration technique: both limitations and benefits are discussed.     

On the distribution of some ordered variables

Abstract

Motivated by a recent article published by Adam and Tawn, we characterize the distribution of two random variables X, Y ordered linearly like X < Y. We suppose that the random variables follow a bivariate extreme value distribution.