Improved approaches to interval estimation of effective doses for a logistic dose-response curve

Asymptotic confidence (delta) intervals and intervals based upon the use of Fieller's theorem are alternative methods for constructing intervals for the <$>gamma<$>% effective doses (ED<$>_gamma<$>). Sitter and Wu (1993) provided a comparison of the two approaches for the ED<$>_{50}<$>, for the case in which a logistic dose response curve is assumed. They showed that the Fieller intervals are generally superior. In this paper, we introduce two new families of intervals, both of which include the delta and Fieller intervals as special cases. In addition we consider interval estimation of the ED<$>_{90}<$> as well as the ED<$>_{50}<$>. We provide a comparison of the various methods for the problem of constructing a confidence interval for the ED<$>_gamma<$>.     

Bayesian estimation and prediction for Weibull model with progressive censoring

This article presents the statistical inferences on Weibull parameters with the data that are progressively type II censored. The maximum likelihood estimators are derived. For incorporation of previous information with current data, the Bayesian approach is considered. We obtain the Bayes estimators under squared error loss with a bivariate prior distribution, and derive the credible intervals for the parameters of Weibull distribution. Also, the Bayes prediction intervals for future observations are obtained in the one- and two-sample cases. The method is shown to be practical, although a computer program is required for its implementation. A numerical example is presented for illustration and some simulation study are performed.     

Bayesian inference for the randomly censored Weibull distribution

In this paper, we consider the Bayesian inference of the unknown parameters of the randomly censored Weibull distribution. A joint conjugate prior on the model parameters does not exist; we assume that the parameters have independent gamma priors. Since closed-form expressions for the Bayes estimators cannot be obtained, we use Lindley's approximation, importance sampling and Gibbs sampling techniques to obtain the approximate Bayes estimates and the corresponding credible intervals. A simulation study is performed to observe the behaviour of the proposed estimators. A real data analysis is presented for illustrative purposes.     

Asymptotic hypothesis test to simultaneously compare the weighted kappa coefficients of multiple binary diagnostic tests in the presence of ignorable missing data

The weighted kappa coefficient of a binary diagnostic test is a measure of the beyond-chance agreement between the diagnostic test and the gold standard, and is a measure that allows us to assess and compare the performance of binary diagnostic tests. In the presence of partial disease verification, the comparison of the weighted kappa coefficients of two or more binary diagnostic tests cannot be carried out ignoring the individuals with an unknown disease status, since the estimators obtained would be affected by verification bias. In this article, we propose a global hypothesis test based on the chi-square distribution to simultaneously compare the weighted kappa coefficients when in the presence of partial disease verification the missing data mechanism is ignorable. Simulation experiments have been carried out to study the type I error and the power of the global hypothesis test. The results have been applied to the diagnosis of coronary disease.     

Simulated annealing for the bounds of Kendall's τ and Spearman's ρ

It has long been known that, for many joint distributions, Kendall's τ and Spearman's ρ have different values, as they measure different aspects of the dependence structure. Although the classical inequalities between Kendall's τ and Spearman's ρ for pairs of random variables are given, the joint distributions which can attain the bounds between Kendall's τ and Spearman's ρ are difficult to find. We use the simulated annealing method to find the bounds for ρ in terms of τ and its corresponding joint distribution which can attain those bounds. Furthermore, using this same method, we find the improved bounds between τ and ρ, which is different from that given by Durbin and Stuart.     

A likelihood ratio test to discriminate exponential–Poisson and gamma distributions

The exponential–Poisson (EP) distribution with scale and shape parameters β>0 and λ∈?, respectively, is a lifetime distribution obtained by mixing exponential and zero-truncated Poisson models. The EP distribution has been a good alternative to the gamma distribution for modelling lifetime, reliability and time intervals of successive natural disasters. Both EP and gamma distributions have some similarities and properties in common, for example, their densities may be strictly decreasing or unimodal, and their hazard rate functions may be decreasing, increasing or constant depending on their shape parameters. On the other hand, the EP distribution has several interesting applications based on stochastic representations involving maximum and minimum of iid exponential variables (with random sample size) which make it of distinguishable scientific importance from the gamma distribution. Given the similarities and different scientific relevance between these models, one question of interest is how to discriminate them. With this in mind, we propose a likelihood ratio test based on Cox's statistic to discriminate the EP and gamma distributions. The asymptotic distribution of the normalized logarithm of the ratio of the maximized likelihoods under two null hypotheses – data come from EP or gamma distributions – is provided. With this, we obtain the probabilities of correct selection. Hence, we propose to choose the model that maximizes the probability of correct selection (PCS). We also determinate the minimum sample size required to discriminate the EP and gamma distributions when the PCS and a given tolerance level based on some distance are before stated. A simulation study to evaluate the accuracy of the asymptotic probabilities of correct selection is also presented. The paper is motivated by two applications to real data sets.     

Adaptation of the jackknifed ridge methods to the linear mixed models

The purpose of this article is to obtain the jackknifed ridge predictors in the linear mixed models and to examine the superiorities, the linear combinations of the jackknifed ridge predictors over the ridge, principal components regression, r?k class and Henderson's predictors in terms of bias, covariance matrix and mean square error criteria. Numerical analyses are considered to illustrate the findings and a simulation study is conducted to see the performance of the jackknifed ridge predictors.     

The Complete Exact Null Distribution of Spearman's Rho for n = 12(1)18

Spearman's rank correlation coefficient, Rho, is a widely used nonparametric measure of association. Complete, exact tables of the null distribution are calculated and presented for n = 12 to 18.