Regenerative Markov Chain Monte Carlo for Any Distribution

While Markov chain Monte Carlo (MCMC) methods are frequently used for difficult calculations in a wide range of scientific disciplines, they suffer from a serious limitation: their samples are not independent and identically distributed. Consequently, estimates of expectations are biased if the initial value of the chain is not drawn from the target distribution. Regenerative simulation provides an elegant solution to this problem. In this article, we propose a simple regenerative MCMC algorithm to generate variates for any distribution.     

CUSUM Hypothesis Tests and Alternative Response Probabilities for Finite Poisson Trials

This article develops a new cumulative sum statistic to identify aberrant behavior in a sequentially administered multiple-choice standardized examination. The examination responses can be described as finite Poisson trials, and the statistic can be used for other applications which fit this framework. The standardized examination setting uses a maximum likelihood estimate of examinee ability and an item response theory model. Aberrant and non aberrant probabilities are computed by an odds ratio analogous to risk adjusted CUSUM schemes. The significance level of a hypothesis test, where the null hypothesis is non-aberrant examinee behavior, is computed with Markov chains. A smoothing process is used to spread probabilities across the Markov states. The practicality of the approach to detect aberrant examinee behavior is demonstrated with results from both simulated and empirical data.     

Analyzing Binomial Data in a Split-Plot Design: Classical Approach or Modern Techniques?

Modeling data that are non-normally distributed with random effects is the major challenge in analyzing binomial data in split-plot designs. Seven methods for analyzing such data using mixed, generalized linear, or generalized linear mixed models are compared for the size and power of the tests. This study shows that analyzing random effects properly is more important than adjusting the analysis for non-normality. Methods based on mixed and generalized linear mixed models hold Type I error rates better than generalized linear models. Mixed model methods tend to have higher power than generalized linear mixed models when the sample size is small.     

Comparing a New Gini Test with Other Symmetry Tests When Median Is Unknown

Although there exists an ample literature on the tests of univariate symmetry, each article provides comparison of few selected competitors only. We are comparing the performance of 15 tests recommended in the literature and two new methods introduced by Auda (2006 Auda (Ouda), H. 2006. New Tests of Univariate Symmetry Based on the Gini Mean Difference, Kalamazoo, MI: Western Michigan University. Ph.D. thesis [Google Scholar]). One of them, rank-based test RS, compares favorably with several existing procedures in controlling the Type I error as well as in power as shown in our comprehensive simulation study. An important novelty in the article are Figs. 1– 3 enabling comparison of Type I error probabilities and power of the 16 tests for 17 null and 19 alternative distributions.     

Further Results on Order Statistics Generated by Two Simulation Methods

Uniform order statistics generated by two simulation methods are compared by means of Pitman’s measure of closeness. This measure, as a probability, is shown to be asymptotically 1/2. Some results are also established for fixed points of the cumulative distribution function (CDF) for a uniform order statistic. These fixed points are important for calculations involving the joint distribution of these order statistics.     

McDonald's ωt,Cronbach's α, and Generalized θ for Composite Reliability of Common Factors Structures

In the common factor model for subtest scores, several reliability coefficients, including Cronbach's α, have been found to be biased. In this article, we introduce a new coefficient, θ_G, or Generalized θ, which is a generalized version of Armor's θ coefficient and is equal to the true reliability when the dimensions are orthogonal and the measures are parallel. We assessed the McDonald's ω_t, α, and θ_G in terms of mean bias, efficiency, and precision using a Monte Carlo simulation. θ_G outperformed ω_t when the factors were orthogonal or nearly orthogonal with low correlations between them.     

Methods for Testing Population Signal-to-Noise Ratio

This article considered several test statistics for testing the population signal-to-noise ratio based on parametric, nonparametric, and modified methods. To compare the performance of the proposed test statistics, a simulation study has been conducted under both symmetric and skewed distributions. The performance of the test statistics is compared based on the empirical size and power of the test. It is evident for large sample that some of our proposed test statistics are performing better in the sense of high power and have been recommended for the researchers.     

One stage multiple comparisons of k-1 treatment mean lifetimes with the control for exponential distributions under heteroscedasticity

Abstract

In survival or reliability data analysis, it is often useful to estimate the quantiles of the lifetime distribution, such as the median time to failure. Different nonparametric methods can construct confidence intervals for the quantiles of the lifetime distributions, some of which are implemented in commonly used statistical software packages. We here investigate the performance of different interval estimation procedures under a variety of settings with different censoring schemes. Our main objectives in this paper are to (i) evaluate the performance of confidence intervals based on the transformation approach commonly used in statistical software, (ii) introduce a new density-estimation-based approach to obtain confidence intervals for survival quantiles, and (iii) compare it with the transformation approach. We provide a comprehensive comparative study and offer some useful practical recommendations based on our results. Some numerical examples are presented to illustrate the methodologies developed.     

Performance of standard imputation methods for missing quality of life data as covariate in survival analysis based on simulations from the International Breast Cancer Study Group Trials VI and VII*

Abstract

Imputation methods for missing data on a time-dependent variable within time-dependent Cox models are investigated in a simulation study. Quality of life (QoL) assessments were removed from the complete simulated datasets, which have a positive relationship between QoL and disease-free survival (DFS) and delayed chemotherapy and DFS, by missing at random and missing not at random (MNAR) mechanisms. Standard imputation methods were applied before analysis. Method performance was influenced by missing data mechanism, with one exception for simple imputation. The greatest bias occurred under MNAR and large effect sizes. It is important to carefully investigate the missing data mechanism.     

Parameter Estimation of Stable Distributions

ABSTRACT

In finance, economics, statistical physics, signal processing, telecommunications, etc., we frequently meet data sets with outliers that transport important information. α-stable distributions are found more suitable in modeling these kind of data. But the lack of simple and effective methods of estimating their parameters limited their applications to wider variety of fields. In this article we develop an unbiased estimator for the stable index α. With the structure of U-statistic, it inherits all the good statistical properties from U-statistics. A consistent estimator of its asymptotic variance is provided. The asymptotic normality of the given estimator holds when using the estimated variance for standardization. Simulation studies are performed. The results support our theory.