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Articles 1 - 30 of 81
Full-Text Articles in Physical Sciences and Mathematics
Equilibrium Problems With Equilibrium Constraints Via Multiobjective Optimization, Boris S. Mordukhovich
Equilibrium Problems With Equilibrium Constraints Via Multiobjective Optimization, Boris S. Mordukhovich
Mathematics Research Reports
The paper concerns a new class of optimization-related problems called Equilibrium Problems with Equilibrium Constraints (EPECs). One may treat them as two level hierarchical problems, which involve equilibria at both lower and upper levels. Such problems naturally appear in various applications providing an equilibrium counterpart (at the upper level) of Mathematical Programs with Equilibrium Constraints (MPECs). We develop a unified approach to both EPECs and MPECs from the viewpoint of multiobjective optimization subject to equilibrium constraints. The problems of this type are intrinsically nonsmooth and require the use of generalized differentiation for their analysis and applications. This paper presents necessary …
Necessary Conditions In Nonsmooth Minimization Via Lower And Upper Subgradients, Boris S. Mordukhovich
Necessary Conditions In Nonsmooth Minimization Via Lower And Upper Subgradients, Boris S. Mordukhovich
Mathematics Research Reports
The paper concerns first-order necessary optimality conditions for problems of minimizing nonsmooth functions under various constraints in infinite-dimensional spaces. Based on advanced tools of variational analysis and generalized differential calculus, we derive general results of two independent types called lower subdifferential and upper subdifferential optimality conditions. The former ones involve basic/limiting subgradients of cost functions, while the latter conditions are expressed via Frechetjregular upper subgradients in fairly general settings. All the upper subdifferential and major lower subdifferential optimality conditions obtained in the paper are new even in finite dimensions. We give applications of general optimality conditions to mathematical programs with …
Optimal Control Of Delayed Differential-Algebraic Inclusions, Boris S. Mordukhovich, Lianwen Wang
Optimal Control Of Delayed Differential-Algebraic Inclusions, Boris S. Mordukhovich, Lianwen Wang
Mathematics Research Reports
This paper concerns constrained dynamic optimization problems governed by delayed differential-algebraic systems. Dynamic constraints in such systems, which are particularly important for engineering applications, are described by interconnected delay-differential inclusions and algebraic equations. We pursue a two-hold goal: to study variational stability of such control systems with respect to discrete approximations and to derive necessary optimality conditions for both delayed differential-algebraic systems and their finite-difference counterparts using modern tools of variational analysis and generalized differentiation. We are not familiar with any results in these directions for differential-algebraic inclusions even in the delay-free case. In the first part of the paper …
The Approximate Maxium Principle In Constrained Optimal Control, Boris S. Mordukhovich, Ilya Shvartsman
The Approximate Maxium Principle In Constrained Optimal Control, Boris S. Mordukhovich, Ilya Shvartsman
Mathematics Research Reports
The paper concerns optimal control problems for dynamic systems governed by a parametric family of discrete approximations of control systems with continuous time. Discrete approximations play an important role in both qualitative and numerical aspects of optimal control and occupy an intermediate position between discrete-time and continuous-time control systems. The central result in optimal control of discrete approximations is the Approximate Maximum Principle (AMP), which is justified for smooth control problems with endpoint constraints under certain assumptions without imposing any convexity, in contrast to discrete systems with a fixed step. We show that these assumptions are essential for the validity …
Optimization And Feedback Control Of Constrained Parabolic Systems Under Uncertain Perturbations, Boris S. Mordukhovich, Ilya Shvartsman
Optimization And Feedback Control Of Constrained Parabolic Systems Under Uncertain Perturbations, Boris S. Mordukhovich, Ilya Shvartsman
Mathematics Research Reports
This paper concerns a minimax control design problem for a class of parabolic systems with nonregular boundary conditions and uncertain distributed perturbations under pointwise control and state constraints. We deal with boundary controllers acting through Dirichlet boundary conditions that are the most challenging for the parabolic dynamics.
Statistical Pronouncements Ii, Shlomo S. Sawilowsky
Statistical Pronouncements Ii, Shlomo S. Sawilowsky
Theoretical and Behavioral Foundations of Education Faculty Publications
No abstract provided.
Deconstructing Arguments From The Case Against Hypothesis Testing, Shlomo S. Sawilowsky
Deconstructing Arguments From The Case Against Hypothesis Testing, Shlomo S. Sawilowsky
Theoretical and Behavioral Foundations of Education Faculty Publications
The main purpose of this article is to contest the propositions that (1) hypothesis tests should be abandoned in favor of confidence intervals, and (2) science has not benefited from hypothesis testing. The minor purpose is to propose (1) descriptive statistics, graphics, and effect sizes do not obviate the need for hypothesis testing, (2) significance testing (reporting p values and leaving it to the reader to determine significance) is subjective and outside the realm of the scientific method, and (3) Bayesian and qualitative methods should be used for Bayesian and qualitative research studies, respectively.
Neumann Boundary Control Of Hyperbolic Equations With Pointwise State Constraints, Boris S. Mordukhovich, Jean-Pierre Raymond
Neumann Boundary Control Of Hyperbolic Equations With Pointwise State Constraints, Boris S. Mordukhovich, Jean-Pierre Raymond
Mathematics Research Reports
We consider optimal control problems for hyperbolic systems with controls in Neumann boundary conditions with pointwise (hard) constraints on control and state functions. Focusing on hyperbolic dynamics governed by the multidimensional wave equation with a nonlinear term, we derive new necessary optimality conditions in the pointwise form of the Pontryagin Maximum Principle for the state-constrained problem under consideration. Our approach is based on modern methods of variational analysis that allows us to obtain refined necessary optimality conditions with no convexity assumptions on integrands in the minimizing cost functional.
Model Comparisons Using Information Measures, C. Mitchell Dayton
Model Comparisons Using Information Measures, C. Mitchell Dayton
Journal of Modern Applied Statistical Methods
Methodologists have criticized the use of significance tests in the behavioral sciences but have failed to provide alternative data analysis strategies that appeal to applied researchers. For purposes of comparing alternate models for data, information-theoretic measures such as Akaike AIC have advantages in comparison with significance tests. Model-selection procedures based on a min(AIC) strategy, for example, are holistic rather than dependent upon a series of sometimes contradictory binary (accept/reject) decisions.
Fortune Cookies, Measurement Error, And Experimental Design, Greogry R. Hancock
Fortune Cookies, Measurement Error, And Experimental Design, Greogry R. Hancock
Journal of Modern Applied Statistical Methods
This article pertains to the theoretical and practical detriments of measurement error in traditional univariate and multivariate experimental design, and points toward modern methods that facilitate greater accuracy in effect size estimates and power in hypothesis testing.
A Comparison Of Equivalence Testing In Combination With Hypothesis Testing And Effect Sizes, Christopher J. Mecklin
A Comparison Of Equivalence Testing In Combination With Hypothesis Testing And Effect Sizes, Christopher J. Mecklin
Journal of Modern Applied Statistical Methods
Equivalence testing, an alternative to testing for statistical significance, is little used in educational research. Equivalence testing is useful in situations where the researcher wishes to show that two means are not significantly different. A simulation study assessed the relationships between effect size, sample size, statistical significance, and statistical equivalence.
Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara
Approximate Bayesian Confidence Intervals For The Variance Of A Gaussian Distribution, Vincent A. R. Camara
Journal of Modern Applied Statistical Methods
The aim of the present study is to obtain and compare confidence intervals for the variance of a Gaussian distribution. Considering respectively the square error and the Higgins-Tsokos loss functions, approximate Bayesian confidence intervals for the variance of a normal population are derived. Using normal data and SAS software, the obtained approximate Bayesian confidence intervals will then be compared to the ones obtained with the well known classical method. The Bayesian approach relies only on the observations. It is shown that the proposed approximate Bayesian approach relies only on the observations. The classical method, that uses the Chi-square statistic, does …
Using Zero-Inflated Count Regression Models To Estimate The Fertility Of U. S. Women, Dudley L. Poston Jr., Sherry L. Mckibben
Using Zero-Inflated Count Regression Models To Estimate The Fertility Of U. S. Women, Dudley L. Poston Jr., Sherry L. Mckibben
Journal of Modern Applied Statistical Methods
In the modeling of count variables there is sometimes a preponderance of zero counts. This article concerns the estimation of Poisson regression models (PRM) and negative binomial regression models (NBRM) to predict the average number of children ever born (CEB) to women in the U.S. The PRM and NBRM will often under-predict zeros because they do not consider zero counts of women who are not trying to have children. The fertility of U.S. white and Mexican-origin women show that zero-inflated Poisson (ZIP) and zero-inflated negative binomial (ZINB) models perform better in many respects than the Poisson and negative binomial models. …
Test Of Homogeneity For Umbrella Alternatives In Dose-Response Relationship For Poisson Variables, Chengjie Xiong, Yan Yan, Ming Ji
Test Of Homogeneity For Umbrella Alternatives In Dose-Response Relationship For Poisson Variables, Chengjie Xiong, Yan Yan, Ming Ji
Journal of Modern Applied Statistical Methods
This article concerns the testing and estimation of a dose-response effect in medical studies. We study the statistical test of homogeneity against umbrella alternatives in a sequence of Poisson distributions associated with an ordered dose variable. We propose a test similar to Cochran-Armitage’s trend test and study the asymptotic null distribution and the power of the test. We also propose an estimator to the vertex point when the umbrella pattern is confirmed and study the performance of the estimator. A real data set pertaining to the number of visible revertant colonies associated with different doses of test agents in an …
Alphabet Letter Recognition And Emergent Literacy Abilities Of Rising Kindergarten Children Living In Low-Income Families, Stephanie Wehry
Alphabet Letter Recognition And Emergent Literacy Abilities Of Rising Kindergarten Children Living In Low-Income Families, Stephanie Wehry
Journal of Modern Applied Statistical Methods
Alphabet letter recognition item responses from 1,299 rising kindergarten children from low-income families were used to determine the dimensionality of letter recognition ability. The rising kindergarteners were enrolled in preschool classrooms implementing a research-based early literary curriculum. Item responses from the TERA-3 subtests were also analyzed. Results indicated alphabet letter recognition was unitary. The ability of boys and younger children was less than girls and older children. Child-level letter recognition was highly associated with TERA-3 measures of letter knowledge and conventions of print. Classroom-level mean letter recognition ability accounted for most of variance in classroom mean TERA-3 scores.
A Note On Mles For Normal Distribution Parameters Based On Disjoint Partial Sums Of A Random Sample, W. J. Hurley
A Note On Mles For Normal Distribution Parameters Based On Disjoint Partial Sums Of A Random Sample, W. J. Hurley
Journal of Modern Applied Statistical Methods
Maximum likelihood estimators are computed for the parameters of a normal distribution based on disjoint partial sums of a random sample. It has application in the disaggregation of financial data.
Deconstructing Arguments From The Case Against Hypothesis Testing, Shlomo S. Sawilowsky
Deconstructing Arguments From The Case Against Hypothesis Testing, Shlomo S. Sawilowsky
Journal of Modern Applied Statistical Methods
The main purpose of this article is to contest the propositions that (1) hypothesis tests should be abandoned in favor of confidence intervals, and (2) science has not benefited from hypothesis testing. The minor purpose is to propose (1) descriptive statistics, graphics, and effect sizes do not obviate the need for hypothesis testing, (2) significance testing (reporting p values and leaving it to the reader to determine significance) is subjective and outside the realm of the scientific method, and (3) Bayesian and qualitative methods should be used for Bayesian and qualitative research studies, respectively.
Conventional And Robust Paired And Independent-Samples T Tests: Type I Error And Power Rates, Katherine Fradette, H. J. Keselman, Lisa Lix, James Algina, Rand R. Wilcox
Conventional And Robust Paired And Independent-Samples T Tests: Type I Error And Power Rates, Katherine Fradette, H. J. Keselman, Lisa Lix, James Algina, Rand R. Wilcox
Journal of Modern Applied Statistical Methods
Monte Carlo methods were used to examine Type I error and power rates of 2 versions (conventional and robust) of the paired and independent-samples t tests under nonnormality. The conventional (robust) versions employed least squares means and variances (trimmed means and Winsorized variances) to test for differences between groups.
Fitting Generalized Linear Mixed Models For Point-Referenced Spatial Data, Armin Gemperli, Penelope Vounatsou
Fitting Generalized Linear Mixed Models For Point-Referenced Spatial Data, Armin Gemperli, Penelope Vounatsou
Journal of Modern Applied Statistical Methods
Non-Gaussian point-referenced spatial data are frequently modeled using generalized linear mixed models (GLMM) with location-specific random effects. Spatial dependence can be introduced in the covariance matrix of the random effects. Maximum likelihood-based or Bayesian estimation implemented via Markov chain Monte Carlo (MCMC) for such models is computationally demanding especially for large sample sizes because of the large number of random effects and the inversion of the covariance matrix involved in the likelihood. We review three fitting procedures, the Penalized Quasi Likelihood method, the MCMC, and the Sampling-Importance-Resampling method. They are assessed in terms of estimation accuracy, ease of implementation, and …
Jmasm9: Converting Kendall’S Tau For Correlational Or Meta-Analytic Analyses, David A. Walker
Jmasm9: Converting Kendall’S Tau For Correlational Or Meta-Analytic Analyses, David A. Walker
Journal of Modern Applied Statistical Methods
Expanding on past research, this study provides researchers with a detailed table for use in meta-analytic applications when engaged in assorted examinations of various r-related statistics, such as Kendall’s tau (τ) and Cohen’s d, that estimate the magnitude of experimental or observational effect. A program to convert from the lesser-used tau coefficient to other effect size indices when conducting correlational or meta-analytic analyses is presented.
P* Index Of Segregation: Distribution Under Reassignment, Charles F. Bond, F. D. Richard
P* Index Of Segregation: Distribution Under Reassignment, Charles F. Bond, F. D. Richard
Journal of Modern Applied Statistical Methods
Students of intergroup relations have measured segregation with a P* index. In this article, we describe the distribution of this index under a stochastic model. We derive exact, closed-form expressions for the mean, variance, and skewness of P* under random segregation. These yield equivalent expressions for a second segregation index: η2. Our analytic results reveal some of the distributional properties of these indices, inform new standardizations of the indices, and enable small-sample significance testing. Two illustrative examples are presented.
A Critical Examination Of The Use Of Preliminary Tests In Two-Sample Tests Of Location, Kimberly T. Perry
A Critical Examination Of The Use Of Preliminary Tests In Two-Sample Tests Of Location, Kimberly T. Perry
Journal of Modern Applied Statistical Methods
This paper explores the appropriateness of testing the equality of two means using either a t test, the Welch test, or the Wilcoxon-Mann-Whitney test for two independent samples based on the results of using two classes of preliminary tests (i.e., tests for population variance equality and symmetry in underlying distributions).
Confidence Intervals For P(X Less Than Y) In The Exponential Case With Common Location Parameter, Ayman Baklizi
Confidence Intervals For P(X Less Than Y) In The Exponential Case With Common Location Parameter, Ayman Baklizi
Journal of Modern Applied Statistical Methods
The problem considered is interval estimation of the stress - strength reliability R = P(Xθ and λ respectively and a common location parameter μ . Several types of asymptotic, approximate and bootstrap intervals are investigated. Performances are investigated using simulation techniques and compared in terms of attainment of the nominal confidence level, symmetry of lower and upper error rates, and expected length. Recommendations concerning their usage are given.
Random Regression Models Based On The Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data, Alfred A. Bartolucci, Shimin Zheng, Sejong Bae, Karan P. Singh
Random Regression Models Based On The Elliptically Contoured Distribution Assumptions With Applications To Longitudinal Data, Alfred A. Bartolucci, Shimin Zheng, Sejong Bae, Karan P. Singh
Journal of Modern Applied Statistical Methods
We generalize Lyles et al.’s (2000) random regression models for longitudinal data, accounting for both undetectable values and informative drop-outs in the distribution assumptions. Our models are constructed on the generalized multivariate theory which is based on the Elliptically Contoured Distribution (ECD). The estimation of the fixed parameters in the random regression models are invariant under the normal or the ECD assumptions. For the Human Immunodeficiency Virus Epidemiology Research Study data, ECD models fit the data better than classical normal models according to the Akaike (1974) Information Criterion. We also note that both univariate distributions of the random intercept and …
Variable Selection For Poisson Regression Model, Felix Famoye, Daniel E. Rothe
Variable Selection For Poisson Regression Model, Felix Famoye, Daniel E. Rothe
Journal of Modern Applied Statistical Methods
Poisson regression is useful in modeling count data. In a study with many independent variables, it is desirable to reduce the number of variables while maintaining a model that is useful for prediction. This article presents a variable selection technique for Poisson regression models. The data used is log-linear, but the methods could be adapted to other relationships. The model parameters are estimated by the method of maximum likelihood. The use of measures of goodness-of-fit to select appropriate variables is discussed. A forward selection algorithm is presented and illustrated on a numerical data set. This algorithm performs as well if …
Type I Error Rates Of Four Methods For Analyzing Data Collected In A Groups Vs Individuals Design, Stephanie Wehry, James Algina
Type I Error Rates Of Four Methods For Analyzing Data Collected In A Groups Vs Individuals Design, Stephanie Wehry, James Algina
Journal of Modern Applied Statistical Methods
Using previous work on the Behrens-Fisher problem, two approximate degrees of freedom tests, that can be used when one treatment is individually administered and one is administered to groups, were developed. Type I error rates are presented for these tests, an additional approximate degrees of freedom test developed by Myers, Dicecco, and Lorch (1981), and a mixed model test. The results indicate that the test that best controls the Type I error rate depends on the number of groups in the group-administered treatment. The mixed model test should be avoided.
A Nonparametric Fitted Test For The Behrens-Fisher Problem, Terry Hyslop, Paul J. Lupinacci
A Nonparametric Fitted Test For The Behrens-Fisher Problem, Terry Hyslop, Paul J. Lupinacci
Journal of Modern Applied Statistical Methods
A nonparametric test for the Behrens-Fisher problem that is an extension of a test proposed by Fligner and Policello was developed. Empirical level and power estimates of this test are compared to those of alternative nonparametric and parametric tests through simulations. The results of our test were better than or comparable to all tests considered.
Example Of The Impact Of Weights And Design Effects On Contingency Tables And Chi-Square Analysis, David A. Walker, Denise Y. Young
Example Of The Impact Of Weights And Design Effects On Contingency Tables And Chi-Square Analysis, David A. Walker, Denise Y. Young
Journal of Modern Applied Statistical Methods
Many national data sets used in educational research are not based on simple random sampling schemes, but instead are constructed using complex sampling designs characterized by multi-stage cluster sampling and over-sampling of some groups. Incorrect results are obtained from statistical analysis if adjustments are not made for the sampling design. This study demonstrates how the use of weights and design effects impact the results of contingency tables and chi-square analysis of data from complex sampling designs.
Correcting Publication Bias In Meta-Analysis: A Truncation Approach, Guillermo Montes, Bohdan S. Lotyczewski
Correcting Publication Bias In Meta-Analysis: A Truncation Approach, Guillermo Montes, Bohdan S. Lotyczewski
Journal of Modern Applied Statistical Methods
Meta-analyses are increasingly used to support national policy decision making. The practical implications of publications bias in meta-analysis are discussed. Standard approaches to correct for publication bias require knowledge of the selection mechanism that leads to publication. In this study, an alternative approach is proposed based on Cohen’s corrections for a truncated normal. The approach makes less assumptions, is easy to implement, and performs well in simulations with small samples. The approach is illustrated with two published meta-analyses.
Comparison Of Viral Trajectories In Aids Studies By Using Nonparametric Mixed-Effects Models, Chin-Shang Li, Hua Liang, Ying-Hen Hsieh, Shiing-Jer Twu
Comparison Of Viral Trajectories In Aids Studies By Using Nonparametric Mixed-Effects Models, Chin-Shang Li, Hua Liang, Ying-Hen Hsieh, Shiing-Jer Twu
Journal of Modern Applied Statistical Methods
The efficacy of antiretroviral therapies for human immunodeficiency virus (HIV) infection can be assessed by studying the trajectory of the changing viral load with treatment time, but estimation of viral trajectory parameters by using the implicit function form of linear and nonlinear parametric models can be problematic. Using longitudinal viral load data from a clinical study of HIV-infected patients in Taiwan, we described the viral trajectories by applying a nonparametric mixed-effects model. We were then able to compare the efficacies of highly active antiretroviral therapy (HAART) and conventional therapy by using Young and Bowman’s (1995) test.