Paul Chiou

An information-theoretic approach to incorporating prior information in binomial sampling

The incorporation of prior information about θ, where θ is the success probability in a binomial sampling model, is an essential feature of Bayesian statistics. Methodology based on information-theoretic concepts is introduced which (a) quantifies the amount of information provided by the sample data relative to that provided by the prior distribution and (b) allows for a ranking of prior distributions with respect to conservativeness, where conservatism refers to restraint of extraneous information about θ which is embedded in any prior distribution. In effect, the most conservative prior distribution from a specified class (each member o f which carries the available prior information about θ) is that prior distribution within the class over which the likelihood function has the greatest average domination. The most conservative prior distributions from five different families of prior distributions over the interval (0,1) including the beta distribution are determined and compared for three situations:...

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.

Estimation of scale parameters for two exponential distributions (reliability theory)

The scale parameter of the exponential distribution is estimated using conditional specification. When there are two censored samples available for estimating the scale parameter, a preliminary test is usually used to determine whether to pool the samples or to use the individual minimum-variance unbiased estimator. This latter estimator (usual preliminary-test estimator) is studied. The optimum levels of significance and their corresponding critical values for the preliminary test are obtained on the basis of the minimax regret criterion. A preliminary-test shrinkage estimator is proposed, and the optimum values of its shrinkage estimator is proposed, and the optimum values of its shrinkage coefficients are obtained. For a mean-square-error criterion of goodness of estimation, the preliminary-test shrinkage estimator is better than the usual preliminary-test estimator. >

Shrinkage estimation of threshold parameter of the exponential distribution (reliability theory)

The authors study the usual preliminary test estimator of the threshold parameter of the exponential distribution in censored samples. The optimal levels of significance and their corresponding critical values for the preliminary test are obtained. The optimal values of shrinkage coefficients for a preliminary test shrinkage estimator are also obtained on the basis of the minimax regret criterion. >

Interval estimation of scale parameters following a pre-test for two exponential distributions

Abstract If two censored samples come from the exponential distributions with identical scale parameters, it is advantageous to pool the two samples to construct a confidence interval for the scale parameter. In practice, when it is uncertain whether these two samples come from the distributions with identical scale parameters, a preliminary test may be used to partially resolve the uncertainty. A confidence interval for the scale parameter following a preliminary test concerning the equality of scale parameters is investigated. This interval is referred to as a pre-test confidence interval. The expected length of the pre-test confidence interval is shorter than that of the usual confidence interval. The coverage probability of the pre-test confidence interval is less than the nominal level. However, at some selected levels of significance, the coverage probability of the pre-test confidence interval is only slightly less than the nominal level but the maximum reduction in expected length is substantial.

Shrinkage estimation of reliability in the exponential distribution

In this paper we propose two shrinkage testimators for the reliability of the exponential distribution and study their properties. The optimum shrinkage coefficients for the shrinkage testimators are obtained based on a regret function and the minimax regret criterion. Shrinkage testimators are compared with a preliminary test estimator and with the usual estimator in terms of mean squared error. The proposed shrinkage testimators are shown to be preferable to the preliminary test estimator and the usual estimator when the prior value of mean life is close to the true mean life.

A Preliminary Test Estimator of Reliability in a Life-Testing Model

This paper proposes a preliminary test estimator for the reliability of an exponential life-testing model. The optimum critical values for preliminary test and their corresponding levels of significance are obtained based on a minimax regret function.

Confidence intervals for the difference between two means

This paper compares three confidence intervals for the difference between two means when the distributions are non-normal and their variances are unknown. The confidence intervals considered are Welch-Satterthwaite confidence interval, the adaptive interval that incorporates a preliminary test (pre-test) of symmetry for the underlying distributions, and the adaptive interval that incorporates the Shapiro-Wilk test for normality as a pre-test. The adaptive confidence intervals use the Welch-Satterthwaite interval if the pre-test fails to reject symmetry (or normality) for both distributions; otherwise, apply the Welch-Satterthwaite confidence interval to the log-transformed data, then transform the interval back. Our study shows that the adaptive interval with pre-test of symmetry has best coverage among the three intervals considered. Simulation studies show that the adaptive interval with pre-test of symmetry performs as well as the Welch-Satterthwaite interval for symmetric distributions. However, for skewed distributions, the adaptive interval with pre-test of symmetry performs better than the Welch-Satterthwaite interval.

Interval estimation of error variance following a preliminary test in one–way random model

A confidence interval for the error variance following a preliminary test in the oneway random model is investigated. This interval is referred to as a pre-test confidence interval. The expected length of the pre-test confidence interval is shorter than that of the usual confidence interval. The coverage probability of the pre–test confidence interval is less than the nominal level. However, at some selected levels of significance, the coverage probability of the pre-test confidence interval is only slightly less than the nominal level but the maximum reduction in expected length is substantial

Shrinkage estimation for the difference between exponential guarantee time parameters

This paper studies the shrinkage estimation for the difference between location parameters of exponential distributions when it is suspected but uncertain whether the two parameters are equal. A pre-test estimator and a shrinkage estimator after pre-test are proposed. Both the suboptimal levels of significance for the pre-test estimator in a special case and suboptimal values of shrinkage coefficients for the shrinkage estimator are obtained based on a regret function.