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Articles 1861 - 1890 of 2316

Full-Text Articles in Physical Sciences and Mathematics

Generalized Differentiation Of Parameter-Dependent Sets And Mappings, Boris S. Mordukhovich, Bingwu Wang Dec 2006

Generalized Differentiation Of Parameter-Dependent Sets And Mappings, Boris S. Mordukhovich, Bingwu Wang

Mathematics Research Reports

The paper concerns new aspects of generalized differentiation theory that plays a crucial role in many areas of modern variational analysis, optimization, and their applications. In contrast to the majority of previous developments, we focus here on generalized differentiation of parameter-dependent objects (sets, set-valued mappings, and nonsmooth functions), which naturally appear, e.g., in parametric optimization and related topics. The basic generalized differential constructions needed in this case are different for those known in parameter-independent settings, while they still enjoy comprehensive calculus rules developed in this paper.

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Optimal Control Of Nonconvex Differential Inclusions, Boris S. Mordukhovich Dec 2006

Optimal Control Of Nonconvex Differential Inclusions, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns new aspects of generalized differentiation theory that plays a crucial role in many areas of modern variational analysis, optimization, and their applications. In contrast to the majority of previous developments, we focus here on generalized differentiation of parameter-dependent objects (sets, set-valued mappings, and nonsmooth functions), which naturally appear, e.g., in parametric optimization and related topics. The basic generalized differential constructions needed in this case are different for those known in parameter-independent settings, while they still enjoy comprehensive calculus rules developed in this paper.

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The Mass Of The Black Hole In The Seyfert 1 Galaxy Ngc 4593 From Reverberation Mapping, Kelly D. Denney, Misty C. Bentz, Bradley M. Peterson, Richard W. Pogge, Edward M. Cackett, Matthias Dietrich, Jeffrey K. J. Fogel, Himel Ghosh, Keith D. Horne, Charles Kuehn, Takeo Minezaki, Christopher A. Onken, Vladimir I. Pronik, Douglas O. Richstone, Sergey G. Sergeev, Marianne Vestergaard, Matthew G. Walker, Yuzuru Yoshii Dec 2006

The Mass Of The Black Hole In The Seyfert 1 Galaxy Ngc 4593 From Reverberation Mapping, Kelly D. Denney, Misty C. Bentz, Bradley M. Peterson, Richard W. Pogge, Edward M. Cackett, Matthias Dietrich, Jeffrey K. J. Fogel, Himel Ghosh, Keith D. Horne, Charles Kuehn, Takeo Minezaki, Christopher A. Onken, Vladimir I. Pronik, Douglas O. Richstone, Sergey G. Sergeev, Marianne Vestergaard, Matthew G. Walker, Yuzuru Yoshii

Physics and Astronomy Faculty Research Publications

We present new observations leading to an improved black hole mass estimate for the Seyfert 1 galaxy NGC 4593 as part of a reverberation-mapping campaign conducted at the MDM Observatory. Cross-correlation analysis of the Hβ emission-line light curve with the optical continuum light curve reveals an emission-line time delay of τcent=3.73+/-0.75 days. By combining this time delay with the Hβ line width, we derive a central black hole mass of MBH=(9.8+/-2.1)×106 Msolar, an improvement in precision of a factor of several over past results.

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Epi-Convergent Discretization Of The Generalizaed Bolza Problem In Dynamic Optimization, Boris S. Mordukhovich, Teemu Pennanen Dec 2006

Epi-Convergent Discretization Of The Generalizaed Bolza Problem In Dynamic Optimization, Boris S. Mordukhovich, Teemu Pennanen

Mathematics Research Reports

The paper is devoted to well-posed discrete approximations of the so-called generalized Bolza problem of minimizing variational functionals defined via extended-real-valued functions. This problem covers more conventional Bolza-type problems in the calculus of variations and optimal control of differential inclusions as well of parameterized differential equations. Our main goal is find efficient conditions ensuring an appropriate epi-convergence of discrete approximations, which plays a significant role in both the qualitative theory and numerical algorithms of optimization and optimal control. The paper seems to be the first attempt to study epi-convergent discretizations of the generalized Bolza problem; it establishes several rather general …

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A Reverberation-Based Mass For The Central Black Hole In Ngc 4151, Misty C. Bentz, Kelly D. Denney, Edward M. Cackett, Matthias Dietrich, Jeffery K. Fogel, Himel Ghosh, Keith Horne, Charles Kuehn, Takeo Minezaki, Christopher A. Onken, Bradley M. Peterson, Richard W. Pogge, Vladimir I. Pronik, Douglas O. Richstone, Sergey G. Sergeev, Marianne Vestergaard, Matthew G. Walker, Yuzuru Yoshii Nov 2006

A Reverberation-Based Mass For The Central Black Hole In Ngc 4151, Misty C. Bentz, Kelly D. Denney, Edward M. Cackett, Matthias Dietrich, Jeffery K. Fogel, Himel Ghosh, Keith Horne, Charles Kuehn, Takeo Minezaki, Christopher A. Onken, Bradley M. Peterson, Richard W. Pogge, Vladimir I. Pronik, Douglas O. Richstone, Sergey G. Sergeev, Marianne Vestergaard, Matthew G. Walker, Yuzuru Yoshii

Physics and Astronomy Faculty Research Publications

We have undertaken a new ground-based monitoring campaign to improve the estimates of the mass of the central black hole in NGC 4151. We measure the lag time of the broad Hβ line response compared to the optical continuum at 5100 Å and find a lag of 6.6+1.1-0.8 days. We combine our data with the recent reanalysis of UV emission lines by Metzroth and coworkers to calculate a weighted mean of the black hole mass, MBH=(4.57+0.57-0.47)×107 Msolar. The absolute calibration of the black hole mass is based on normalization of …

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Cooling Of The Quasi-Persistent Neutron Star X-Ray Transients Ks 1731-260 And Mxb 1659-29, Edward M. Cackett, Rudy Wijnands, Manuel Linares, Jon M. Miller, Jeroen Homan, Walter H. G. Lewin Oct 2006

Cooling Of The Quasi-Persistent Neutron Star X-Ray Transients Ks 1731-260 And Mxb 1659-29, Edward M. Cackett, Rudy Wijnands, Manuel Linares, Jon M. Miller, Jeroen Homan, Walter H. G. Lewin

Physics and Astronomy Faculty Research Publications

We present Chandra and XMM-Newton X-ray observations that monitor the neutron star cooling of the quasi-persistent neutron star X-ray transients KS 1731-260 and MXB 1659-29 for approximately 4 yr after these sources returned to quiescence from prolonged outbursts. In both sources the outbursts were long enough to significantly heat the neutron star crust out of thermal equilibrium with the core. We analyse the X-ray spectra by fitting absorbed neutron star atmosphere models to the observations. The results of our analysis strengthen the preliminary findings of Wijnands et al. that in both sources the neutron star crust cools down very rapidly …

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Multiobjective Optimization Problems With Equilibrium Constraints, Boris S. Mordukhovich Oct 2006

Multiobjective Optimization Problems With Equilibrium Constraints, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to new applications of advanced tools of modern variational analysis and generalized differentiation to the study of broad classes of multiobjective optimization problems subject to equilibrium constraints in both finite-dimensional and infinite-dimensional settings. Performance criteria in multiobjectivejvector optimization are defined by general preference relationships satisfying natural requirements, while equilibrium constraints are described by parameterized generalized equations/variational conditions in the sense of Robinson. Such problems are intrinsically nonsmooth and are handled in this paper via appropriate normal/coderivativejsubdifferential constructions that exhibit full calculi. Most of the results obtained are new even in finite dimensions, while the case of …

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Necessary Conditions In Multiobjective Optimization With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich Sep 2006

Necessary Conditions In Multiobjective Optimization With Equilibrium Constraints, Truong Q. Bao, Panjak Gupta, Boris S. Mordukhovich

Mathematics Research Reports

In this paper we study multiobjective optimization problems with equilibrium constraints (MOECs) described by generalized equations in the form 0 is an element of the set G(x,y) + Q(x,y), where both mappings G and Q are set-valued. Such models particularly arise from certain optimization-related problems governed by variational inequalities and first-order optimality conditions in nondifferentiable programming. We establish verifiable necessary conditions for the general problems under consideration and for their important specifications using modern tools of variational analysis and generalized differentiation. The application of the obtained necessary optimality conditions is illustrated by a numerical example from bilevel programming with convex …

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Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?, Haijun Wu, Zhimin Zhang Aug 2006

Can We Have Superconvergent Gradient Recovery Under Adaptive Meshes?, Haijun Wu, Zhimin Zhang

Mathematics Research Reports

We study adaptive finite element methods for elliptic problems with domain corner singularities. Our model problem is the two dimensional Poisson equation. Results of this paper are two folds. First, we prove that there exists an adaptive mesh (gauged by a discrete mesh density function) under which the recovered.gradient by the Polynomial Preserving Recovery (PPR) is superconvergent. Secondly, we demonstrate by numerical examples that an adaptive procedure with a posteriori error estimator based on PPR does produce adaptive meshes satisfy our mesh density assumption, and the recovered gradient by PPR is indeed supercoveregent in the adaptive process.

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Xmm-Newton Discovery Of The X-Ray Transient Xmmu J181227.8-181234 In The Galactic Plane, Edward M. Cackett, Rudy Wijnands, Ron Remillard Jul 2006

Xmm-Newton Discovery Of The X-Ray Transient Xmmu J181227.8-181234 In The Galactic Plane, Edward M. Cackett, Rudy Wijnands, Ron Remillard

Physics and Astronomy Faculty Research Publications

We report the discovery of an X-ray transient, observed in outburst with XMM-Newton on 2003 March 20, and with position (J2000, approximate positional error 2arcsec). No known source is present at this position and the source was not detected during published ROSAT or ASCA observations of that region. However, the source may be associated with 1H1812-182 detected by HEAO 1, although the error bars on the HEAO 1 position are very large and the two sources could also be unrelated. Therefore, we name the source XMMU J181227.8-181234. Initially, the source was not detected using the All-Sky Monitor (ASM) on-board the …

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Charactarizations Of Linear Suboptimality For Mathematical Programs With Equilibrium Constraints, Boris S. Mordukhovich Jul 2006

Charactarizations Of Linear Suboptimality For Mathematical Programs With Equilibrium Constraints, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to the study of a new notion of linear suboptimality in constrained mathematical programming. This concept is different from conventional notions of solutions to optimization-related problems, while seems to be natural and significant from the viewpoint of modern variational analysis and applications. In contrast to standard notions, it admits complete characterizations via appropriate constructions of generalized differentiation in nonconvex settings. In this paper we mainly focus on various classes of mathematical programs with equilibrium constraints (MPECs), whose principal role has been well recognized in optimization theory and its applications. Based on robust generalized differential calculus, we …

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Methods Of Variational Analysis In Multiobjective Optimization, Boris S. Mordukhovich Jun 2006

Methods Of Variational Analysis In Multiobjective Optimization, Boris S. Mordukhovich

Mathematics Research Reports

The paper concerns new applications of advanced methods of variational analysis and generalized differentiation to constrained problems of multiobjective/vector optimization. We pay the main attention to general notions of optimal solutions for multiobjective problems that are induced by geometric concepts. of extremality in variational analysis while covering various notions of Pareto and other type of optimality/efficiency conventional in multiobjective optimization. Based on the extremal principles in variational analysis and on appropriate tools of generalized differentiation with well-developed calculus rules, we derive necessary optimality conditions for broad classes of constrained multiobjective problems in the framework of infinite-dimensional spaces. Applications of variational …

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A Chandra X-Ray Observation Of The Globular Cluster Terzan 1, E. M. Cackett, R. Wijnands, C. O. Heinke, D. Pooley, W. H. G. Lewin, J. E. Grindlay, P. D. Edmonds, P. G. Jonker, J. M. Miller Jun 2006

A Chandra X-Ray Observation Of The Globular Cluster Terzan 1, E. M. Cackett, R. Wijnands, C. O. Heinke, D. Pooley, W. H. G. Lewin, J. E. Grindlay, P. D. Edmonds, P. G. Jonker, J. M. Miller

Physics and Astronomy Faculty Research Publications

We present a ~19-ks Chandra Advanced CCD Imaging Spectrometer (ACIS)-S observation of the globular cluster Terzan 1. 14 sources are detected within 1.4arcmin of the cluster centre with two of these sources predicted to be not associated with the cluster (background active galactic nuclei or foreground objects). The neutron star X-ray transient, X1732-304, has previously been observed in outburst within this globular cluster with the outburst seen to last for at least 12yr. Here, we find four sources that are consistent with the ROSAT position for this transient, but none of the sources are fully consistent with the position of …

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Pietro Paoli, Italian Algebraist, John L. Cuzzocrea, Shlomo S. Sawilowsky May 2006

Pietro Paoli, Italian Algebraist, John L. Cuzzocrea, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Pietro Paoli was a leading Italian mathematician in the late 18th century. His signed letter pertaining to the death of astronomer Giuseppe Antonio Slop is translated from Italian to flowing (American) English.

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Joseph Liouville’S ‘Mathematical Works Of Évariste Galois’, Shlomo S. Sawilowsky May 2006

Joseph Liouville’S ‘Mathematical Works Of Évariste Galois’, Shlomo S. Sawilowsky

Theoretical and Behavioral Foundations of Education Faculty Publications

Liouville’s 1846 introduction to the mathematical works of Galois is translated from French to flowing (American) English. It gave an overview of the tragic circumstances of the undergraduate mathematician whose originality led to major advances in abstract Algebra.

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Variational Analysis In Nonsmooth Optimization And Discrete Optimal Control, Boris S. Mordukhovich May 2006

Variational Analysis In Nonsmooth Optimization And Discrete Optimal Control, Boris S. Mordukhovich

Mathematics Research Reports

The paper is devoted to applications of modern methods of variational· analysis to constrained optimization and control problems generally formulated in infinite-dimensional spaces. The main attention is paid to the study of problems with nonsmooth structures, which require the usage of advanced tools of generalized differentiation. In this way we derive new necessary optimality conditions in optimization problems with functional and. operator constraints and then apply them to optimal control problems governed by discrete-time inclusions in infinite dimensions. The principal difference between finite-dimensional and infinite-dimensional frameworks of optimization and control consists of the "lack of compactness" in infinite dimensions, which …

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Confidence Intervals For An Effect Size When Variances Are Not Equal, James Algina, H. J. Keselman, Randall D. Penfield May 2006

Confidence Intervals For An Effect Size When Variances Are Not Equal, James Algina, H. J. Keselman, Randall D. Penfield

Journal of Modern Applied Statistical Methods

Confidence intervals must be robust in having nominal and actual probability coverage in close agreement. This article examined two ways of computing an effect size in a two-group problem: (a) the classic approach which divides the mean difference by a single standard deviation and (b) a variant of a method which replaces least squares values with robust trimmed means and a Winsorized variance. Confidence intervals were determined with theoretical and bootstrap critical values. Only the method that used robust estimators and a bootstrap critical value provided generally accurate probability coverage under conditions of nonnormality and variance heterogeneity in balanced as …

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Limitations Of The Analysis Of Variance, Phillip I. Good, Clifford E. Lunneborg May 2006

Limitations Of The Analysis Of Variance, Phillip I. Good, Clifford E. Lunneborg

Journal of Modern Applied Statistical Methods

Conditions under which the analysis of variance will yield inexact p-values or would be inferior in power to a permutation test are investigated. The findings for the one-way design are consistent with and extend those of Miller (1980).

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Ancova: A Robust Omnibus Test Based On Selected Design Points, Rand R. Wilcox May 2006

Ancova: A Robust Omnibus Test Based On Selected Design Points, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

Many robust analogs of the classic analysis of covariance method have been proposed. One approach, when comparing two independent groups, uses selected design points and then compares the groups at each design point using some robust method for comparing measures of location. So, if K design points are of interest, K tests are performed. There are rather obvious ways of performing, instead, an omnibus test that for all K points, no differences between the groups exist. One of the main results here is that several variations of these methods can perform very poorly in simulations. An alternative approach, based in …

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Penalized Splines For Longitudinal Data With An Application In Aids Studies, Hua Liang, Yuanhui Xiao May 2006

Penalized Splines For Longitudinal Data With An Application In Aids Studies, Hua Liang, Yuanhui Xiao

Journal of Modern Applied Statistical Methods

A penalized spline approximation is proposed in considering nonparametric regression for longitudinal data. Standard linear mixed-effects modeling can be applied for the estimation. It is relatively simple, efficiently computed, and robust to the smooth parameters selection, which are often encountered when local polynomial and smoothing spline techniques are used to analyze longitudinal data set. The method is extended to time-varying coefficient mixed-effects models. The proposed methods are applied to data from an AIDS clinical study. Biological interpretations and clinical implications are discussed. Simulation studies are done to illustrate the proposed methods.

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Choosing Smoothing Parameters For Exponential Smoothing: Minimizing Sums Of Squared Versus Sums Of Absolute Errors, Terry E. Dielman May 2006

Choosing Smoothing Parameters For Exponential Smoothing: Minimizing Sums Of Squared Versus Sums Of Absolute Errors, Terry E. Dielman

Journal of Modern Applied Statistical Methods

When choosing smoothing parameters in exponential smoothing, the choice can be made by either minimizing the sum of squared one-step-ahead forecast errors or minimizing the sum of the absolute onestep- ahead forecast errors. In this article, the resulting forecast accuracy is used to compare these two options.

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The Efficiency Of Ols In The Presence Of Auto-Correlated Disturbances In Regression Models, Samir Safi, Alexander White May 2006

The Efficiency Of Ols In The Presence Of Auto-Correlated Disturbances In Regression Models, Samir Safi, Alexander White

Journal of Modern Applied Statistical Methods

The ordinary least squares (OLS) estimates in the regression model are efficient when the disturbances have mean zero, constant variance, and are uncorrelated. In problems concerning time series, it is often the case that the disturbances are correlated. Using computer simulations, the robustness of various estimators are considered, including estimated generalized least squares. It was found that if the disturbance structure is autoregressive and the dependent variable is nonstochastic and linear or quadratic, the OLS performs nearly as well as its competitors. For other forms of the dependent variable, rules of thumb are presented to guide practitioners in the choice …

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Understanding Eurasian Convergence: Application Of Kohonen Self-Organizing Maps, Joel I. Deichmann, Abdolreza Eshghi, Dominique Haughton, Selin Sayek, Nicholas Teebagy, Heikki Topi May 2006

Understanding Eurasian Convergence: Application Of Kohonen Self-Organizing Maps, Joel I. Deichmann, Abdolreza Eshghi, Dominique Haughton, Selin Sayek, Nicholas Teebagy, Heikki Topi

Journal of Modern Applied Statistical Methods

Kohonen self-organizing maps (SOMs) are employed to examine economic and social convergence of Eurasian countries based on a set of twenty-eight socio-economic measures. A core of European Union states is identified that provides a benchmark against which convergence of post-socialist transition economies may be judged. The Central European Visegrád countries and Baltics show the greatest economic convergence to Western Europe, while other states form clusters that lag behind. Initial conditions on the social dimension can either facilitate or constrain economic convergence, as discovered in Central Europe vis-à-vis the Central Asian Republics. Disquiet in the convergence literature is resolved by providing …

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Analysis Of Type-Ii Progressively Hybrid Censored Competing Risks Data, Debasis Kundu, Avijit Joarder May 2006

Analysis Of Type-Ii Progressively Hybrid Censored Competing Risks Data, Debasis Kundu, Avijit Joarder

Journal of Modern Applied Statistical Methods

A Type-II progressively hybrid censoring scheme for competing risks data is introduced, where the experiment terminates at a pre-specified time. The likelihood inference of the unknown parameters is derived under the assumptions that the lifetime distributions of the different causes are independent and exponentially distributed. The maximum likelihood estimators of the unknown parameters are obtained in exact forms. Asymptotic confidence intervals and two bootstrap confidence intervals are also proposed. Bayes estimates and credible intervals of the unknown parameters are obtained under the assumption of gamma priors on the unknown parameters. Different methods have been compared using Monte Carlo simulations. One …

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Jmasm23: Cluster Analysis In Epidemiological Data (Matlab), Andrés M. Alonso May 2006

Jmasm23: Cluster Analysis In Epidemiological Data (Matlab), Andrés M. Alonso

Journal of Modern Applied Statistical Methods

Matlab functions for testing the existence of time, space and time-space clusters of disease occurrences are presented. The classical scan test, the Ederer, Myers and Mantel’s test, the Ohno, Aoki and Aoki’s test, and the Knox’s test are considered.

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Properties Of Bound Estimators On Treatment Effect Heterogeneity For Binary Outcomes, Edward J. Mascha, Jeffrey M. Albert May 2006

Properties Of Bound Estimators On Treatment Effect Heterogeneity For Binary Outcomes, Edward J. Mascha, Jeffrey M. Albert

Journal of Modern Applied Statistical Methods

Variability in individual causal effects, treatment effect heterogeneity (TEH), is important to the interpretation of clinical trial results, regardless of the marginal treatment effect. Unfortunately, it is usually ignored. In the setting of two-arm randomized studies with binary outcomes, there are estimators for bounds on the probability of control success and treatment failure for an individual, or the treatment risk. Here, those bounds were refined and the sampling properties were assessed using simulations of correlated multinomial data via the Dirichlet multinomial. Results indicated low bias and mean squared error. Moderate to high intraclass correlation (ICC) and large numbers of clusters …

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Two New Unbiased Point Estimates Of A Population Variance, Matthew E. Elam May 2006

Two New Unbiased Point Estimates Of A Population Variance, Matthew E. Elam

Journal of Modern Applied Statistical Methods

Two new unbiased point estimates of an unknown population variance are introduced. They are compared to three known estimates using the mean-square error (MSE). A computer program, which is available for download at http://program.20m.com, is developed for performing calculations for the estimates.

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Multiple Comparison Procedures, Trimmed Means And Transformed Statistics, Rhonda K. Kowalchuk, H. J. Keselman, Rand R. Wilcox, James Algina, James Algina, James Algina May 2006

Multiple Comparison Procedures, Trimmed Means And Transformed Statistics, Rhonda K. Kowalchuk, H. J. Keselman, Rand R. Wilcox, James Algina, James Algina, James Algina

Journal of Modern Applied Statistical Methods

A modification to testing pairwise comparisons that may provide better control of Type I errors in the presence of non-normality is to use a preliminary test for symmetry which determines whether data should be trimmed symmetrically or asymmetrically. Several pairwise MCPs were investigated, employing a test of symmetry with a number of heteroscedastic test statistics that used trimmed means and Winsorized variances. Results showed improved Type I error control than competing robust statistics.

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Confidence Intervals On Subsets May Be Misleading, Juliet Popper Shaffer May 2006

Confidence Intervals On Subsets May Be Misleading, Juliet Popper Shaffer

Journal of Modern Applied Statistical Methods

No abstract provided.

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The Effect On Type I Error And Power Of Various Methods Of Resolving Ties For Six Distribution-Free Tests Of Location, Bruce R. Fay May 2006

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.

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