Statistical Theory Commons^™

The Effect On Type I Error And Power Of Various Methods Of Resolving Ties For Six Distribution-Free Tests Of Location, Bruce R. Fay

Journal of Modern Applied Statistical Methods

The impact on Type I error robustness and power for nine different methods of resolving ties was assessed for six distribution-free statistics with four empirical data sets using Monte Carlo techniques. These statistics share an underlying assumption of population continuity such that samples are assumed to have no equal data values (no zero difference–scores, no tied ranks). The best results across all tests and combinations of simulation parameters were obtained by randomly resolving ties, although there were exceptions. The method of dropping ties and reducing the sample size performed poorly.

Nonparametric Bayesian Multiple Comparisons For Dependence Parameter In Bivariate Exponential Populations, M. Masoom Ali, J. S. Cho, Munni Begum

Journal of Modern Applied Statistical Methods

A nonparametric Bayesian multiple comparisons problem (MCP) for dependence parameters in I bivariate exponential populations is studied. A simple method for pairwise comparisons of these parameters is also suggested. The methodology by Gopalan and Berry (1998) is extended using Dirichlet process priors, applied in the form of baseline prior and likelihood combination to provide the comparisons. Computation of the posterior probabilities of all possible hypotheses are carried out through a Markov Chain Monte Carlo, Gibbs sampling, due to the intractability of analytic evaluation. The process of MCP for the dependent parameters of bivariate exponential populations is illustrated with a numerical …

Entropy Criterion In Logistic Regression And Shapley Value Of Predictors, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Entropy criterion is used for constructing a binary response regression model with a logistic link. This approach yields a logistic model with coefficients proportional to the coefficients of linear regression. Based on this property, the Shapley value estimation of predictors’ contribution is applied for obtaining robust coefficients of the linear aggregate adjusted to the logistic model. This procedure produces a logistic regression with interpretable coefficients robust to multicollinearity. Numerical results demonstrate theoretical and practical advantages of the entropy-logistic regression.

Comparison Of Some Simple Estimators Of The Lognormal Parameters Based On Censored Samples, Baklizi Ayman, Mohammed Al-Haj Ebrahem

Journal of Modern Applied Statistical Methods

Point estimation of the parameters of the lognormal distribution with censored data is considered. The often employed maximum likelihood estimator does not exist in closed form and iterative methods that require very good starting points are needed. In this article, some techniques of finding closed form estimators to this situation are presented and extended. An extensive simulation study is carried out to investigate and compare the performance of these techniques. The results show that some of them are highly efficient as compared with the maximum likelihood estimator.

Statistical Pronouncements V, Jmasm Editors

Journal of Modern Applied Statistical Methods

No abstract provided.

Properties Of The Gar(1) Model For Time Series Of Counts, Vasiliki Karioti, Chrys Caroni

Journal of Modern Applied Statistical Methods

Models for time series count data include several proposed by Zeger and Qaqish (1988), subsequently generalized into the GARMA family. The GAR(1) model is examined in detail. The maximum likelihood estimation of the parameters will be discussed and the properties of Pearson and randomized residuals will be examined.

Variance Estimation And Construction Of Confidence Intervals For Gee Estimator, Shenghai Zhang, Mary E. Thompson

Journal of Modern Applied Statistical Methods

The sandwich estimator, also known as the robust covariance matrix estimator, has achieved increasing use in the statistical literature as well as with the growing popularity of generalized estimating equations (GEE). A modified sandwich variance estimator is proposed, and its consistency and efficiency are studied. It is compared with other variance estimators, such as a model based estimator, the sandwich estimator and a corrected sandwich estimator. Confidence intervals for regression parameters based on these estimators are discussed. Simulation studies using clustered data to compare the performance of variance estimators are reported.

Jmasm22: A Convenient Way Of Generating Normal Random Variables Using Generalized Exponential Distribution, Debasis Kundu, Anubhav Manglick

Journal of Modern Applied Statistical Methods

A convenient method to generate normal random variable using a generalized exponential distribution is proposed. The new method is compared with the other existing methods and it is observed that the proposed method is quite competitive with most of the existing methods in terms of the K − S distances and the corresponding p-values.

A Combined Individuals And Moving Range Control Chart, Michael B. C. Khoo, S. H. Quah, C. K. Ch'ng

Journal of Modern Applied Statistical Methods

An individuals control chart is usually used to monitor shifts in the process mean when it is not possible to form subgroups. The moving range of two successive process measures is used as the basis for estimating the process variability. Similar to the case of the X − R and X − S charts, the individualsmoving range (I-MR) charts are used simultaneously in the monitoring of the process mean and variance respectively for individual observations, requiring maintaining two different charts. In this article, a new approach is suggested where the measurements of both the process mean and variance are plotted …

A Combined Standard Deviation Based Data Clustering Algorithm, Kuttiannan Thangavel, Durairaj Ashok Kumar

Journal of Modern Applied Statistical Methods

The clustering problem has been widely studied because it arises in many knowledge management oriented applications. It aims at identifying the distribution of patterns and intrinsic correlations in data sets by partitioning the data points into similarity clusters. Traditional clustering algorithms use distance functions to measure similarity centroid, which subside the influences of data points. Hence, in this article a novel non-distance based clustering algorithm is proposed which uses Combined Standard Deviation (CSD) as measure of similarity. The performance of CSD based K-means approach, called K-CSD clustering algorithm, is tested on synthetic data sets. It compared favorably to widely used …

The Use Of Hierarchical Ancova In Curriculum Studies, Show-Mann Liou, Chao-Ying Joanne Peng

Journal of Modern Applied Statistical Methods

Many educational studies are carried out in intact settings, such as classrooms or groups in which individual data were collected before and after a treatment. Researchers advocate either the use of individual scores as the unit of analysis or class means. Both approaches suffer from conceptual and methodological limitations. In this article, the use of hierarchical ANCOVA for analyzing quasiexperimental data including baseline measures is designed and promoted. It is illustrated with a realworld data set collected from a curriculum study. Results showed that the hierarchical ANCOVA is a conceptually and methodologically sound approach, and is better than ANCOVA based …

Estimating The Integrated Likelihood Via Posterior Simulation Using The Harmonic Mean Identity, Adrian E. Raftery, Michael A. Newton, Jaya M. Satagopan, Pavel N. Krivitsky

Memorial Sloan-Kettering Cancer Center, Dept. of Epidemiology & Biostatistics Working Paper Series

The integrated likelihood (also called the marginal likelihood or the normalizing constant) is a central quantity in Bayesian model selection and model averaging. It is defined as the integral over the parameter space of the likelihood times the prior density. The Bayes factor for model comparison and Bayesian testing is a ratio of integrated likelihoods, and the model weights in Bayesian model averaging are proportional to the integrated likelihoods. We consider the estimation of the integrated likelihood from posterior simulation output, aiming at a generic method that uses only the likelihoods from the posterior simulation iterations. The key is the …

Measuring Inequality: Statistical Inference Theory With Applications, Mihaela Paun

Doctoral Dissertations

In this dissertation we develop statistical inference for the Atkinson index, one of the measures of inequality used in studying economic inequality.

Specifically, we construct empirical estimators for the Atkinson index, both in the parametric and nonparametric case, and derive formulas for the asymptotic variances for the estimators. These statistics are used for testing hypothesis and constructing confidence intervals for the Atkinson index. We test the validity and the robustness of the asymptotic theory, by simulations (using R, a language and environment for statistical computing and graphics), in the case of one and two populations. In addition to proving asymptotic …

The Two-Sample Problem For Failure Rates Depending On A Continuous Mark: An Application To Vaccine Efficacy, Peter B. Gilbert, Ian W. Mckeague, Yanqing Sun

UW Biostatistics Working Paper Series

The efficacy of an HIV vaccine to prevent infection is likely to depend on the genetic variation of the exposing virus. This paper addresses the problem of using data on the HIV sequences that infect vaccine efficacy trial participants to 1) test for vaccine efficacy more powerfully than procedures that ignore the sequence data; and 2) evaluate the dependence of vaccine efficacy on the divergence of infecting HIV strains from the HIV strain that is contained in the vaccine. Because hundreds of amino acid sites in each HIV genome are sequenced, it is natural to treat the divergence (defined in …

Evaluating Prediction Rules For T-Year Survivors With Censored Regression Models, Hajime Uno, Tianxi Cai, Lu Tian, L.J. Wei

Harvard University Biostatistics Working Paper Series

Suppose that we are interested in establishing simple, but reliable rules for predicting future t-year survivors via censored regression models. In this article, we present inference procedures for evaluating such binary classification rules based on various prediction precision measures quantified by the overall misclassification rate, sensitivity and specificity, and positive and negative predictive values. Specifically, under various working models we derive consistent estimators for the above measures via substitution and cross validation estimation procedures. Furthermore, we provide large sample approximations to the distributions of these nonsmooth estimators without assuming that the working model is correctly specified. Confidence intervals, for example, …

Multiple Tests Of Association With Biological Annotation Metadata, Sandrine Dudoit, Sunduz Keles, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a general and formal statistical framework for the multiple tests of associations between known fixed features of a genome and unknown parameters of the distribution of variable features of this genome in a population of interest. The known fixed gene-annotation profiles, corresponding to the fixed features of the genome, may concern Gene Ontology (GO) annotation, pathway membership, regulation by particular transcription factors, nucleotide sequences, or protein sequences. The unknown gene-parameter profiles, corresponding to the variable features of the genome, may be, for example, regression coefficients relating genome-wide transcript levels or DNA copy numbers to possibly censored biological and …

Regression Analysis For The Partial Area Under The Roc Curve, Tianxi Cai, Lori E. Dodd

Harvard University Biostatistics Working Paper Series

No abstract provided.

Addressing The Gaps—Promise And Performance, Synthesis And Purity, Large-N And Small-N: A Response To Moore, Todd Landman

Human Rights & Human Welfare

A response to:

Moore, W. (2006). Synthesis v. purity and large-N studies: How might we assess the gap between promise and performance? Human Rights, Human Welfare, 6(1).