A comparison of methods for studentizing the sample median

Various methods for “Studentizing” the sample median are com-pared on the basis of a Monte Carlo study. Several of the methods do rather poorly while two, the bootstrap and the standardized length of a distribution free confidence interval, behave accept-ably acrors a wide range of sample sizes and several distributions of varying tail length. These two methods seem to agree closely with the distribution free confidence intervals and moreover, un-like these intervals, the methods can be extended to a method of accurate inference for λ₁ regreasion.     

A comparison of estimation techniques for the three parameter pareto distribution

This paper compares minimum distance estimation with best linear unbiased estimation to determine which technique provides the most accurate estimates for location and scale parameters as applied to the three parameter Pareto distribution. Two minimum distance estimators are developed for each of the three distance measures used (Kolmogorov, Cramer‐von Mises, and Anderson‐Darling) resulting in six new estimators. For a given sample size 6 or 18 and shape parameter 1(1)4, the location and scale parameters are estimated. A Monte Carlo technique is used to generate the sample sets. The best linear unbiased estimator and the six minimum distance estimators provide parameter estimates based on each sample set. These estimates are compared using mean square error as the evaluation tool. Results show that the best linear unbaised estimator provided more accurate estimates of location and scale than did the minimum estimators tested.     

Steady-state Gibbs sampler estimation for lung cancer data

This paper is based on the application of a Bayesian model to a clinical trial study to determine a more effective treatment to lower mortality rates and consequently to increase survival times among patients with lung cancer. In this study, Qian et al. [13 J. Qian, D.K. Stangl, and S. George, A Weibull model for survival data: Using prediction to decide when to stop a clinical trial, in Bayesian Biostatistics, D. Berry and D. Stangl, eds., Marcel Dekker, New York, 1996, pp. 187–205. [Google Scholar]] strived to determine if a Weibull survival model can be used to decide whether to stop a clinical trial. The traditional Gibbs sampler was used to estimate the model parameters. This paper proposes to use the independent steady-state Gibbs sampling (ISSGS) approach, introduced by Dunbar et al. [3 M. Dunbar, H.M. Samawi, R. Vogel, and L. Yu, A more efficient Gibbs sampler estimation using steady state simulation: Application to public health studies, J. Stat. Simul. Comput. 10.1080/00949655.2013.770857.[Taylor &; Francis Online] , [Google Scholar]], to improve the original Gibbs sampler in multidimensional problems. It is demonstrated that ISSGS provides accuracy with unbiased estimation and improves the performance and convergence of the Gibbs sampler in this application.     

Bayesian Transformation Models for Multivariate Survival Data

In this paper, we propose a general class of Gamma frailty transformation models for multivariate survival data. The transformation class includes the commonly used proportional hazards and proportional odds models. The proposed class also includes a family of cure rate models. Under an improper prior for the parameters, we establish propriety of the posterior distribution. A novel Gibbs sampling algorithm is developed for sampling from the observed data posterior distribution. A simulation study is conducted to examine the properties of the proposed methodology. An application to a data set from a cord blood transplantation study is also reported.     

Simple Robust Tests for Autocorrelated Errors in Time Series Design Intervention Models

A simple, robust test for the autocorrelation parameter in an intervention time-series model (AB design) is proposed. It is analogous to the traditional tests and can easily be computed by using the freeware R. In the same way as traditional tests of autocorrelation are based on least squares (LS) fits of a linear model, our robust test is based on the highly efficient Wilcoxon fit of the linear model. We present the results of a Monte Carlo study which show that our robust test inherits the good efficiency properties of this Wilcoxon fit. Its empirical power is only slightly less than the empirical power of the least squares test over situations with normally distributed errors while it exhibited much more power over situations with error distributions having tails heavier than those of a normal distribution. It also showed robustness of validity over all null situations simulated. We also present the results of the application of our test to a real data set which illustrates the robustness of our test.     

Uniform Distributions on the Integers: A connection to the Bernouilli Random Walk

Associate to each subset of the integers its almost sure limiting relative frequency under the Bernouilli random walk, if it has one. The resulting probability space is purely finitely additive, and uniform in the sense of residue classes and shift-invariance. However, it is not uniform in the sense of limiting relative frequency.     

A uniform central limit theorem for neural network-based autoregressive processes with applications to change-point analysis

We consider an autoregressive process with a nonlinear regression function that is modelled by a feedforward neural network. First, we derive a uniform central limit theorem which is useful in the context of change-point analysis. Then, we propose a test for a change in the autoregression function which – by the uniform central limit theorem – has asymptotic power one for a large class of alternatives including local alternatives not restricted to the correctly specified model.     

A restricted subset selection procedure for Weibull populations

Consider k(k ≥ 2) two-parameter Weibull populations. We want to select a subset of the populations not exceeding m in size such that the subset contains at least ? of the t best populations. We have proposed a procedure which uses either the maximum likelihood estimators or ‘simplified’ linear estimators of the parameters. The estimators are based on type II censored data. The ranking of the populations is done by comparing their reliabilities at a certain fixed time. In selected cases the constants for the procedure are tabulated using Monte Carlo methods.     

Acknowledgement

We gratefully acknowledge the partial support of the National Institute of Environmental Health Sciences through Training Grant #T32 ESO 7018 and Research Grant #ROI ESO 2286, also the partial support of Special Projects funded by COllncil for Tobacco Research - U.S.A., Inc.