Physical Sciences and Mathematics Commons^™

Local Power For Combining Independent Tests In The Presence Of Nuisance Parameters For The Logistic Distribution, Walid A. Abu-Dayyeh, Z. R. Al-Rawi, M. M. A. Al-Momani

Journal of Modern Applied Statistical Methods

Four combination methods of independent tests for testing a simple hypothesis versus one-sided alternative are considered viz. Fisher, the logistic, the sum of P-values and the inverse normal method in case of logistic distribution. These methods are compared via local power in the presence of nuisance parameters for some values of α using simple random sample.

X-Ray Variability During The Quiescent State Of The Neutron Star X-Ray Transient In The Globular Cluster Ngc 6440, Edward M. Cackett, Rudy Wijnands, Craig O. Heinke, Peter D. Edmonds, Walter H. G. Lewin, David Pooley, Jonathan E. Grindlay, Peter G. Jonker, Jon M. Miller

Physics and Astronomy Faculty Research Publications

The globular cluster NGC 6440 is known to harbor a bright neutron star X-ray transient. We observed the globular cluster with Chandra on two occasions when the bright transient was in its quiescent state, in 2000 July and 2003 June (both observations were made nearly 2 yr after the end of their preceding outbursts). The quiescent spectrum during the first observation is well represented by a two-component model (a neutron star atmosphere model plus a power-law component that dominates at energies above 2 keV). During the second observation (which was roughly of equal duration to the first observation) we found …

Comparison Of Two-Dimensional And Three-Dimensional Simulations Of Dense Nonaqueous Phase Liquids (Dnapls): Migration And Entrapment Of A Nonuniform Permeability Field, John A. Christ, Lawrence D. Lemke, Linda M. Abriola

Environmental Science and Geology Faculty Research Publications

The influence of reduced dimensionality (two-dimensional (2-D) versus 3-D) on predictions of dense nonaqueous phase liquid (DNAPL) infiltration and entrapment in statistically homogeneous, nonuniform permeability fields was investigated using the University of Texas Chemical Compositional Simulator (UTCHEM), a 3-D numerical multiphase simulator. Hysteretic capillary pressure–saturation and relative permeability relationships implemented in UTCHEM were benchmarked against those of another lab-tested simulator, the Michigan-Vertical and Lateral Organic Redistribution (M-VALOR). Simulation of a tetrachloroethene spill in 16 field-scale aquifer realizations generated DNAPL saturation distributions with approximately equivalent distribution metrics in two and three dimensions, with 2-D simulations generally resulting in slightly higher maximum …

Gap Labeling, Claude Schochet

Mathematics Faculty Research Publications

This joint review covers:

Moulay-Tahar Benameur and Hervé Oyono-Oyono, Gap-labelling for quasi-crystals (proving a conjecture by J. Bellissard). (English summary) Operator algebras and mathematical physics, (Constanţa, 2001), 11-22, Theta, Bucharest, 2003.

Jerome Kaminker and Ian Putnam, A proof of the gap labeling conjecture, Michigan Mathematical Journal 51(3) (2003), 537-546.

Jean Bellisard, Riccardo Benedetti and Jean-Marc Gambaudo, Spaces of tilings, finite telescopic approximations, and gap-labeling, Communications in Mathematical Physics 261(1) (2006), 1-41.

The gap labeling theorem was originally conjectured by Bellissard [in From number theory to physics (Les Houches, 1989), 538-630, Springer, Berlin, 1992; MR1221111 (94e:46120)]. …

Penalty Approximation And Analytical Characterization Of The Problem Of Super-Replication Under Portfolio Constraints, Alain Bensoussan, Nizar Touzi, José Luis Menaldi

Mathematics Faculty Research Publications

In this paper, we consider the problem of super-replication under portfolio constraints in a Markov framework. More specifically, we assume that the portfolio is restricted to lie in a convex subset, and we show that the super-replication value is the smallest function which lies above the Black-Scholes price function and which is stable for the so-called face lifting operator. A natural approach to this problem is the penalty approximation, which not only provides a constructive smooth approximation, but also a way to proceed analytically.

Influence Of Hydraulic Property Correlation On Predicted Dense Nonaqueous Phase Liquid Source Zone Architecture, Mass Recovery And Contaminant Flux, Lawrence D. Lemke, Linda M. Abriola, John R. Lang

Environmental Science and Geology Faculty Research Publications

Organic liquid saturation distributions resulting from a simulated tetrachloroethene (PCE) spill were generated with alternative models of spatially varying aquifer properties for a statistically homogeneous, nonuniform sand aquifer. The distributions were analyzed to quantify DNAPL source zone characteristics and then incorporated as initial conditions for simulated PCE recovery using surfactant-enhanced aquifer remediation (SEAR). The predicted evolution of the spatial distribution of DNAPL saturations or source zone ‘‘architectures’’ and associated remediation efficiencies are strongly influenced by the spatial correlation of aquifer parameters and multiphase flow constitutive relationships. Model predictions suggest that removal of 60 to 99% of entrapped PCE can reduce …

Scattering Of Low- To Intermediate-Energy Positrons From Molecular Hydrogen, David D. Reid, William B. Klann, J. M. Wadehra

Physics and Astronomy Faculty Research Publications

Using a complex model potential, we have calculated the total, integrated elastic, momentum transfer, absorption, and differential cross sections for positrons scattered from molecular hydrogen. The widely available software package GAUSSIAN is used to generate the radial electronic charge density of the molecule which is used to produce the interaction potentials. The quasifree absorption potential, previously developed and used for positron-atom scattering, is extended to positron scattering from molecular targets. It is shown that this model potential approach produces accurate results even into the low-energy regime.

A Conversation With R. Clifford Blair On The Occasion Of His Retirement, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

An interview was conducted on 23 November 2003 with R. Clifford Blair on the occasion on his retirement from the University of South Florida. This article is based on that interview. Biographical sketches and images of members of his academic genealogy are provided.

Assessing Treatment Effects In Randomized Longitudinal Two-Group Designs With Missing Observations, James Algina, H. J. Keselman

Journal of Modern Applied Statistical Methods

SAS’s PROC MIXED can be problematic when analyzing data from randomized longitudinal two-group designs when observations are missing over time. Overall (1996, 1999) and colleagues found a number of procedures that are effective in controlling the number of false positives (Type I errors) and are yet sensitive (powerful) to detect treatment effects. Two favorable methods incorporate time in study and baseline scores to model the missing data mechanism; one method was a single-stage PROC MIXED ANCOVA solution and the other was a two-stage endpoint analysis using the change scores as dependent scores. Because the twostage approach can lack sensitivity to …

Type I Error Rates For A One Factor Within-Subjects Design With Missing Values, Miguel A. Padilla, James Algina

Journal of Modern Applied Statistical Methods

Missing data are a common problem in educational research. A promising technique, that can be implemented in SAS PROC MIXED and is therefore widely available, is to use maximum likelihood to estimate model parameters and base hypothesis tests on these estimates. However, it is not clear which test statistic in PROC MIXED performs better with missing data. The performance of the Hotelling- Lawley-McKeon and Kenward-Roger omnibus test statistics on the means for a single factor withinsubject ANOVA are compared. The results indicate that the Kenward-Roger statistic performed better in terms of keeping the Type I error close to the nominal …

Size And Power Of The Reset Test As Applied To Systems Of Equations: A Bootstrap Approach, Ghazi Shukur, Panagiotis Mantalos

Journal of Modern Applied Statistical Methods

The size and power of various generalization of the RESET test for functional misspecification are investigated, using the “Bootsrap critical values”, in systems ranging from one to ten equations. The properties of 8 versions of the test are studied using Monte Carlo methods. The results are then compared with another study of Shukur and Edgerton (2002), in which they used the asymptotic critical values instead and found that in general only one version of the tests works well regarding size properties. In our study, when applying the bootstrap critical values, we find that all the tests exhibits correct size even …

Variance Stabilizing Power Transformation For Time Series, Victor M. Guerrero, Rafael Perera

Journal of Modern Applied Statistical Methods

A confidence interval was derived for the index of a power transformation that stabilizes the variance of a time-series. The process starts from a model-independent procedure that minimizes a coefficient of variation to yield a point estimate of the transformation index. The confidence coefficient of the interval is calibrated through a simulation.

Multivariate Contrasts For Repeated Measures Designs Under Assumption Violations, Lisa M. Lix, Aynslie M. Hinds

Journal of Modern Applied Statistical Methods

Conventional and approximate degrees of freedom procedures for testing multivariate interaction contrasts in groups by trials repeated measures designs were compared under assumption violation conditions. Procedures were based on either least-squares or robust estimators. Power generally favored test procedures based on robust estimators for non-normal distributions, but was influenced by the degree of departure from non-normality, definition of power, and magnitude of the multivariate effect size.

Interval Estimation For The Scale Parameter Of Burr Type X Distribution Based On Grouped Data, Amjad D. Al-Nasser, Ayman Baklizi

Journal of Modern Applied Statistical Methods

The application of some bootstrap type intervals for the scale parameter of the Burr type X distribution with grouped data is proposed. The general asymptotic confidence interval procedure (Chen & Mi, 2001) is studied. The performance of these intervals is investigated and compared. Some of the bootstrap intervals give better performance for situations of small sample size and heavy censoring.

An Algorithm And Code For Computing Exact Critical Values For The Kruskal-Wallis Nonparametric One-Way Anova, Sikha Bagui, Subhash Bagui

Journal of Modern Applied Statistical Methods

In this article, an algorithm and code to compute exact critical values (or percentiles) for Kruskal-Wallis test on k independent treatment populations with equal or unequal sample sizes using Visual Basic (VB.NET) is provided. This program has the ability to calculate critical values for any k , sample sizes (n_i ) , and significance level (α ) . An exact critical value table for k = 4 is also developed. The table will be useful to practitioners since it is not available in standard nonparametric statistics texts. The program can also be used to compute any other …

Pseudo-Random Number Generation In R For Commonly Used Multivariate Distributions, Hakan Demirtas

Journal of Modern Applied Statistical Methods

An increasing number of practitioners and applied statisticians have started using the R programming system in recent years for their computing and data analysis needs. As far as pseudo-random number generation is concerned, the built-in generator in R does not contain multivariate distributions. In this article, R routines for widely used multivariate distributions are presented.

Confidence Intervals On Subsets May Be Misleading, Juliet Popper Shaffer

Journal of Modern Applied Statistical Methods

A combination of hypothesis testing and confidence interval construction is often used in social and behavioral science studies. Sometimes confidence intervals are computed or reported only if a null hypothesis is rejected, perhaps to see whether the range of values is of practical importance. Sometimes they are constructed or reported only if a null hypothesis is accepted, in order to assess the range of plausible nonnull values due to inadequate power to detect them. Even if always computed, they are interpreted differently, depending on whether the null value is or is not included. Furthermore, many studies in which the null …

Mentoring Doctoral Students: A Personal Perspective, Bruce W. Hall

Journal of Modern Applied Statistical Methods

In this brief essay, I reflect on the mentoring process based on advising over thirty doctoral students in measurement, evaluation, and research. There is considerable cause for optimism, and it is among the professors’ highest honor to mentor the doctoral student.

On A Simple Method For Analyzing Multivariate Survival Data Using Sample Survey Methods, Pingfu Fu, J. Sunil Rao

Journal of Modern Applied Statistical Methods

A simple technique is illustrated for analyzing multivariate survival data. The data situation arises when an individual records multiple survival events, or when individuals recording single survival events are grouped into clusters. Past work has focused on developing new methods to handle such data. Here, we use a connection between Poisson regression and survival modeling and a cluster sampling approach to adjust the variance estimates. The approach requires parametric assumption for the marginal hazard function, but avoids specification of a joint multivariate survival distribution. A simulation study demonstrates the proposed approach is a competing method of recent developed marginal approaches …

Monte Carlo Evaluation Of Ordinal D With Improved Confidence Interval, Du Feng, Norman Cliff

Journal of Modern Applied Statistical Methods

This article reports a Monte Carlo evaluation of ordinal statistic d with modified confidence intervals (CI) for location comparison of two independent groups under various conditions. Type I error rate, power, and coverage of CI of d were compared to those of the Welch's t-test.

Confidence Elicitation And Anchoring In The Respondent-Generated Intervals (Rgi) Protocol, Liping Chu, S. James Press, Judith M. Tanur

Journal of Modern Applied Statistical Methods

The Respondent-Generated Intervals protocol (RGI) has been used to have respondents recall the answer to a factual question by giving not only a point estimate but also bounds within which they feel it is almost certain that the true value of the quantity being reported upon falls. The RGI protocol is elaborated in this article with the goal of improving the accuracy of the estimators by introducing cueing mechanisms to direct confident (and thus presumably accurate) respondents to give shorter intervals and less confident (and thus presumably less accurate) respondents to give longer ones.

A Note On Extending Scheffé’S Modified Multiple-Comparison Procedure To Other Analysis Situations, Xinyue Zhou, Joel R. Levin

Journal of Modern Applied Statistical Methods

This article extends Scheffé’s modified (sequential) multiple-comparison procedure in one-way analysisof- variance to other analysis situations, including interaction comparisons in factorial ANOVA designs, tests of partial regression coefficients in multiple-regression analysis, and comparisons of means in onefactor multivariate analyses of variance. Researchers who are concerned with maintaining familywise Type I error rates while increasing statistical power relative to the original (simultaneous) Scheffé-based procedures are encouraged to consider these improved multiple-comparison methods.

A Modification Of The Em Algorithm To Estimate An Andersen-Gill Gamma Frailty Model For Multivariate Failure Time Data, Maria Antònia Barceló, Marc Saez

Journal of Modern Applied Statistical Methods

A modification of the Andersen-Gill gamma shared frailty model is presented. The variance of the frailty is directly modeled by means of a generalized linear model, the EM algorithm is modified in order to simultaneously estimate a semiparametric model for the failure times and a model for the variance of the frailty. A simulation study is conducted to evaluate the performance of the proposed algorithm (EMB algorithm) and compared with other methods, a marginal model, and a conditional model. Multivariate data from a nosocomial infection study is used to illustrate the methods. The EMB fit turned out to be better …

An Overview Of The Respondent-Generated Intervals (Rgi) Approach To Sample Surveys, S. James Press, Judith M. Tanur

Journal of Modern Applied Statistical Methods

This article brings together many years of research on the Respondent-Generated Intervals (RGI) approach to recall in factual sample surveys. Additionally presented is new research on the use of RGI in opinion surveys and the use of RGI with gamma-distributed data. The research combines Bayesian hierarchical modeling with various cognitive aspects of sample surveys.

Statistics And Technology: Reflections On 35 Years Of Change, James J. Higgins

Journal of Modern Applied Statistical Methods

From the days when statistical calculations were done on mechanical calculators to today, technology has transformed the discipline of statistics. More than just giving statisticians the power to crunch numbers, it has fundamentally changed the way we teach, do research, and consult. In this article, I give some examples of this from my 35 years as an academic statistician.

“Teaching” In Honor Of Cliff Blair, Howard Stoker

Journal of Modern Applied Statistical Methods

In this article, I conceptualize teaching as the profession of facilitating and stimulating learning. As “teachers”, we help students acquire learning skills that they may expand on later in their life. I review fifteen principles that facilitate effective learning.

Optimal Control Of Semilinear Evolution Inclusions Via Discrete Approximations, Boris S. Mordukhovich, Dong Wang

Mathematics Research Reports

This paper studies a Mayer type optimal control problem with general endpoint constraints for semilinear unbounded evolution inclusions in reflexive and separable Banach spaces. First, we construct a sequence of discrete approximations to the original optimal control problem for evolution inclusions and prove that optimal solutions to discrete approximation problems uniformly converge to a given optimal solution for the original continuous-time problem. Then, based on advanced tools of generalized differentiation, we derive necessary optimality conditions for discrete-time problems under fairly general assumptions. Combining these results with recent achievements of variational analysis in infinite-dimensional spaces, we establish new necessary optimality conditions …

A New Goodness-Of-Fit Test For Item Response Theory, John H. Neel

Journal of Modern Applied Statistical Methods

Chi-square techniques for testing goodness-of-fit in item response theory are shown to give incorrect results. A new measure, CB, based on cumulants is proposed which avoids the arbitrary nature of interval creation found in chi-square techniques. The distribution of CB is estimated using Monte Carlo techniques and critical values for testing goodness-of-fit are given.

Modeling Incomplete Longitudinal Data, Hakan Demirtas

Journal of Modern Applied Statistical Methods

This article presents a review of popular parametric, semiparametric and ad-hoc approaches for analyzing incomplete longitudinal data.

Aligned Rank Tests As Robust Alternatives For Testing Interactions In Multiple Group Repeated Measures Designs With Heterogeneous Covariances, Xiaosheng Lei, Janet K. Holt, T. Mark Beasley

Journal of Modern Applied Statistical Methods

Data simulation was used to investigate whether tests performed on aligned ranks (Beasley, 2002) could be used as robust alternatives to parametric methods for testing a split-plot interaction with non-normal data and heterogeneous covariance matrices. Results indicated the aligned rank method do not have any distinct advantage over parametric methods in this situation.