Statistics and Probability Commons^™

A Robust Two-Sample Procedure To Estimate A Shift Parameter, Feridun Tasdan

Dissertations

This study estimates the location shift parameter in the two-sample problem. The classical method, Least Square(LS), obtains the shift parameter estimate under the normality assumption. A departure from normality assumption makes the estimate inefficient and unreliable. One alternative to the least square estimate is Hodges-Lehmann (HL) estimate which uses Wilcoxon ranks to estimate the shift parameter. This estimate is robust against contaminations and large outliers. The proposed method in this study combines two samples and uses convolution technique to find a density function for the combined sample. This new density function is later used in the construction of the log …

Spearman Rank Regression, Jason C. Parcon

Dissertations

The main purpose of this dissertation is to obtain an estimate of the slope parameter in a regression model that is robust to outlying values in both the x - and Y-spaces. The least squares method, though known to be optimal for normal errors, can yield estimates with infinitely large MSE's if the error distribution is thick-tailed. Regular rank-based methods like the Wilcoxon method are known to be robust to outlying values in the Y -space, but it is still grossly affected by outlying values in x -space.

This dissertation derives an estimate of the slope from an estimating …

New Graphical Approach On The Analysis Of Experimental Data, Suha Sari

Dissertations

This study presents a new graphical method to identify significant effects in factorial experiments. The proposed methods are obtained for the different cases in which the design can be of full factorial or fractional factorial and the factor levels can be pure or mixed.

We focus on the different decomposition methods, for example orthogonal components system and orthogonal contrast method, to make use of the chisquare plot which requires that the sums of squares are of the same degrees of freedom. Examples and simulations illustrating the different cases of the procedure are presented.

A Comparison Of Different Schemes For Selecting And Estimating Score Functions Based On Residuals, Ali A. Al-Shomrani

Dissertations

In a linear model when the errors follow a normal distribution, least squares methodology is most powerful. However, when the assumption of normality of the error distribution is not met then there exist methods which are more powerful than least squares methods. Rank-based methods form one such class. These methods depend on the selection of a score function [varphi]( u ). The correct choice of [varphi] leads to an optimal (efficient) analysis, but its selection depends on the error distribution which is not known.

In this thesis, we explore different schemes for score selection. Some of these schemes are functions …

On Rank-Based Considerations For Generalized Linear Models And Generalized Estimating Equation Models, Diana R. Cucos

Dissertations

This study discusses rank-based robust methods for estimation of parameters and hypotheses testing in the generalized linear models (GLM) and generalized estimating equations (GEE) setting. The robust estimates are obtained by minimizing a Wilcoxon drop in dispersion function for linear or nonlinear regression models. In addition, diagnostic tools for outliers and influential observations are being developed. These models are generalizations of linear and nonlinear models. They allow for both nonlinear mean functions and heteroscedasticity of their random errors. This makes them quite useful in practice. Rank-based inference has been developed for linear models over the last thirty years. This inference …

Resolvability In Graphs, Varaporn Saenpholphat

Dissertations

The distance d (u, v ) between two vertices u and v in a connected graph G is the length of a shortest u - v path in G . For an ordered set W = { w1 , w2 , [Special characters omitted.] &cdots; , wk } of vertices in G and a vertex v of G , the code of v with respect to W is the k -vector cW (v ) = (d ( v, w1 ),d (v, w 2 ), [Special characters omitted.] &cdots; , d …

Robust Residuals And Diagnostics In Autoregressive Time Series, Kirk W. Anderson

Dissertations

One of the goals of model diagnostics is outlier detection. In particular, we would like to use the residuals, appropriately standardized, to “flag” outliers. Hopefully, our (robust) procedure has yielded a fit that resists undue influence by outlying points, while simultaneously drawing attention to these interesting points via residual analysis. In this study we consider several different methods of standardizing the residuals resulting from autoregression. A large sample approximation for the variance of rank-based first order autoregressive time series residuals is developed. This provides studentized residuals, specific to the time series model and estimation procedure. Simulation studies are presented that …

New Statitstical Methods For The Estimation Of The Mean And Standard Deviation From Normally Distributed Censored Samples, Abou El-Makarim Abd El-Alim Aboueissa

Dissertations

The main objective of this dissertation is to estimate the mean /x and standard deviation cr of a normal population from left-censored samples. We have developed new methods for calculating estimates for the mean and standard deviation of a normal population from left-censored samples. Some of these methods based on traditional estimating procedures. A new method of obtaining the Cohen maximum likelihood estimates for fx and cr without the aid of an auxiliary table will be introduced. This new method will be used to extend Cohen table of estimating the Cohen A-parameter that is required for calculating the maximum likelihood …

Visualization Methods: A Comparative Study Of New, Traditional And Robust Procedures, Kimberly Crimin

Dissertations

Two major goals in discriminant analysis are discrimination and classification. In discrimination, the goal is to describe graphically (visualization) different features of several known groups. In classification, the goal is to allocate unknown observations to one of several known groups. We have developed new visualization procedures based on traditional estimating procedures and also on robust estimating procedures. We have further developed robust classification procedures. We propose several robust classification procedures based on coordinatewise and affine equivariant, rank-based robust estimates. Empirical studies are performed over many different error distributions. These studies result in empirical efficiencies of the robust and traditional procedures. …

Nonlinear Regression Based On Ranks, Asheber Abebe

Dissertations

This study presents robust methods for estimating parameters of nonlinear regression models. The proposed methods obtain estimates by minimizing rankbased dispersions instead of the Euclidean norm. We focus on the Wilcoxon and generalized signed-rank dispersion functions. Asymptotic properties of the estimators are established under mild regularity conditions similar to those used in least squares and least absolute deviations estimation. The study also shows that by considering the generalized signed-rank dispersion we obtain a class of estimators that encompasses most of the existing popular nonlinear regression estimators. As in linear models, these rank-based procedures provide estimators that are highly efficient. This …

Empirical Spectral Analysis Of Random Number Generators, David Zeitler

Dissertations

Computer simulation procedures have become a staple of research and development in many fields, including statistics. The generation of pseudo random number sequences is the core of computer simulation procedures. Validity of research results often depend on the underlying validity of the generator being used.

In this work we develop the machinery for a class of tests of spatial uniformity based on a multi-dimensional Fourier transform of the empirical probability density function. The test can be adapted to specific requirements and has the added advantage that it has computational complexity that is relatively independent of the number of data points …

A Comparison Of Methods For Detection Of Qualitative Interaction In Multicenter Trials, Boyd Jay Hanson

Dissertations

This research evaluated and compared three methods for the detection of qualitative treatment-by-center interaction proposed by Azzalini and Cox, Gail and Simon and Ciminera et al., through the analysis of simulated data for multicenter studies of two and three centers with two treatments. The effect of unequal sample size and the presence of an overall treatment effect on characteristics of the methods were examined.

The approach, underlying assumptions and theory of the three methods differ. For this study, they were adapted to establish a common basis for evaluation, thus allowing a meaningful comparison of the methods. For the test presented …

An Investigation Into Relationships Between Alternative Assessment And Pre-Service Elementary Teachers’ Beliefs About Mathematics, David Charles Coffey

Dissertations

The purpose of this study was to examine how including alternative assessments in a reform-based mathematics course affects pre-service teachers’ mathematical beliefs. A single section of a mathematics course designed for elementary education majors that employed three different alternative assessments was the setting for the study.

A pre- and post-belief survey completed by students enrolled in the section under study represented the first level of data collection and analysis. The results of the pre-belief survey guided the selection of seven informants from the section and provided belief statements for the informants to verify during subsequent interviews. Based on the data …

Rainbow Ramsey Numbers, Linda Eroh

Dissertations

No abstract provided.

Perturbed Hamiltonian System Of Two Parameters With Several Turning Points, Myeong Joon Ann

Dissertations

No abstract provided.

Surface Models Of Finite Geometries, Ramon Manuel Figueroa-Centeno

Dissertations

The standard non-Euclidean geometries, hyperbolic geometry and elliptical geometry, both arise by negating the parallel postulate of Euclid. Both these geometries share with Euclidean geometries an infinitude of points and lines. But also possible are many finite geometries. Among these are the class of projective geometries PG(m,q) of projective dimension m (m > 2) and the k-configurations. These mathematical objects, although primarily geometric in nature, provide related structures of combinatorial interest: block designs. These have applications in scheduling problems and the design of experiments for statistical analysis. Recently, A. T. White has added a topological flavor to the study …

Statistical Graphics: Applications To The R And Gr Methods In Linear Models, Mei Huang Wang

Dissertations

Statistical graphics combine statistics and graphics together to visually display analytical statistical results. They present information in a way that is very easy to understand and, furthermore, they frequently reveal information that is hidden from numerical summaries. Our purpose of this study is to explore the field of statistical graphics by investigating their application to statistical methods in the context of the R and GR methods in linear models. We consider the problems of score selection, R-diagnostics, and comparison of the R- and GR-fits.

We have developed a user friendly program which uses dynamic graphics and a user interface to …

Random Cayley Maps, Michelle Schultz

Dissertations

Determining the orientable surfaces on which a given graph can be imbedded is the central problem of topological graph theory. The natural setting for studying this problem is random topological graph theory, where a probability model is defined on the space of all labeled 2-cell imbeddings of a connected graph. The major focus of this dissertation is the study of Cayley maps in the setting of random topological graph theory.

A Cayley graph provides a representation of a finite group and a fixed generating set for the group. A Cayley map is an imbedding of a Cayley graph whose vertex …

A Computer Simulation Of The Rotary Vacuum Filter Brown Stock Washing System Using Distribution Sampling, Edison G. Yiu

Masters Theses

A probabilistic model was utilized to simulate the brown stock washing system's error due to process variability and measurement noise. Mass balances of the washing system were performed using distribution sampling. This model relies on a nonlinear relationship between displacement and dilution, which permitted the generation of displacement ratio based upon wash liquor ratio. Experimental trials were performed on a pilotscale rotary vacuum single-stage washer. Nonlinear first-order relationship appears to characterize a pilotscale washer adequately. Differences were observed between the means and standard deviations of the measured results compared to the simulation output. Future work is needed to identify the …

An Integrated Simulation Model Development Environment For Slam Ii Using Object-Oriented Paradigm, Rizvan Erol

Masters Theses

An integrated simulation model development environment was implemented to assist the modeler by automating certain activities of simulation modeling. The system included interactive model definition, experimental design, automatic simulation program generation in SLAM II. Object-oriented paradigm at software development stage was extensively used to conceptualize the structure, and rules of the SLAM II language in order to generate efficient, and modular program code. The present system targeted modeling of various probabilistic inventory control system problems. The remarkable advantages of the system were rapid model development time, and achieving reliable program code without requiring any knowledge in SLAM II. Object-oriented programming …

Common Moment Sets Of Complementary Graphs, Hang Chen

Dissertations

Two sequences of nonnegative integers have the k^th common moment if they have equal sums of k^th powers. We intend to study common moment sets of the degree sequences of complementary graphs, and similarly, of the score sequences of complementary tournaments.

In Chapter I, we first study common moment sets of arbitrary sequences of nonnegative integers. Some basic concepts are introduced. The relations between characteristic functions and initial common moments are discovered. We extend Hua’s discussion of the Tarry-Escott problem. We conclude that any finite subset of nonnegative integers can be a common moment set of some sequences, and conversely, …

The Application Of A Statistical Trend Analysis Program To Ground-Water Quality Monitoring Data From Eight Western Michigan Solid Waste Landfills, Amy Decosta Lachance

Masters Theses

A statistical analysis and interpretation of ground-water chemistry data from eight landfills in Western Michigan was performed. Data were collected over approximately the past ten years, pursuant to the requirements of Michigan's Solid Waste Management Act. A statistical regression model was used to reduce the data to identifiable trends and estimated magnitudes. These results were analyzed with respect to each landfill's characteristics and hydrogeological setting. Comparisons were made concerning the landfills' relative potential for environmental harm. Also, the effectiveness and applicability of this model to the analysis of ground-water monitoring data was assessed.

It was concluded that this analysis and …

A Progressive Disease Model For Doubly-Censred Bivariate Survival Data That Accommodates Covariate Information, Hilmi F. Yahya

Dissertations

A model for the natural history of a progressive disease is developed. The model has three disease states and can be expressed as the joint distribution of two survival random variables.

Covariate information is incorporated into the model using the proportional hazards model for the marginal distributions. The model will also accommodate data with observations which are censored on one or both of the survival random variables.

The likelihood function for censored data is exhibited for finding the maximum likelihood estimates of the parameters and their standard errors for testing the effects of the covariates. The method used to obtain …

Coefficients Of Multiple Determination Based On Rank Estimates, Lee D. Witt

Dissertations

No abstract provided.

Robust Rank Analysis For Multivariate Linear Models, James Buddy Davis

Dissertations

Three robust rank procedures are considered to test the multivariate linear hypothesis HBK = 0. In the least squares setting, the Lawley-Hotelling trace criterion provides a UMP when the covariance structure is known. Our work reflects the theoretical structure of the Lawley-Hotelling test with robust rank analogues.

The Lawley-Hotelling test has an asymptotic chi-square distribution when the covariance structure is estimated. The trace criterion can be written in three algebraically equivalent forms: a quadratic test based on full model estimates, a quadratic test based on reduced model residuals and a test based on the drop in the least squares dispersion …

The Design And Analysis Of Drug Combination Experiments, Thomas J. Vidmar

Dissertations

Past literature concerning drug combination studies is reviewed. This literature has both biological and statistical origins. The justification of the logit transformation for dichotomous responses in a linear models framework is made by observing its similarities to models proposed by others. Using the logistic linear model, optimal experimental designs are derived. Methods for obtaining parameter estimates are discussed as are diagnostic techniques for logistic regression. Two new robust techniques for logistic regression are proposed and compared to a robust technique suggested in the literature via Monte Carlo simulation. Finally, estimation of the median effective dose (ED50) and the resulting confidence …

A Computer Simulation Study Of Seven Pairwise Comparison Procedures: Imbalanced Case, Wayne S. Petroelje

Dissertations

No abstract provided.

A Comparison Of The Kuder Richardson Formula 20 And Kappa As Estimates Of The Reliability Of Criterion-Referenced Tests, Judith E. Moyer

Dissertations

No abstract provided.

The Extended Tukey Procedure Compared To The Scheffe And Bonferroni Procedures, Wilber B. Emmert

Masters Theses

No abstract provided.