Statistics and Probability Commons^™

Estimating Familial Correlations Using A Kotz Type Density, Amal Helu

Mathematics & Statistics Theses & Dissertations

Two useful familial correlations often used to study the resemblance between the family members are the sib-sib correlation (ρ_ss) and the mom-sib or parent-sib correlation (ρ_ps). Since their introduction early in the last century by Galton, Fisher and others, many improved estimators of these correlations have been suggested in the literature. Several moment based estimators as well as the maximum likelihood estimators under the assumption of multivariate normality have been extensively studied and compared by various authors. However, the performance of these estimators when the data are not from multivariate normal distribution is poor. In this …

Dimensionality Reduction Using Non-Linear Principal Components Analysis, Tara Singh

Electrical & Computer Engineering Theses & Dissertations

Advances in data collection and storage capabilities during the past decades have led to an information overload in most sciences. Traditional statistical methods break down partly because of the increase in the number of observations, but mostly because of the increase in the number of variables associated with each observation. While certain methods can construct predictive models with high accuracy from high-dimensional data, it is still of interest in many applications to reduce the dimension of the original data prior to any modeling of the data. Patterns in the data can be hard to find in data of high dimensionality, …

Efficient Unbiased Estimating Equations For Analyzing Structured Correlation Matrices, Yihao Deng

Mathematics & Statistics Theses & Dissertations

Analysis of dependent continuous and discrete data has become an active area of research. For normal data, correlations fully quantify the dependence. And historically, maximum likelihood method has been very successful to estimate the correlations and unbiased estimating equation approach has become a popular alternative when there may be a departure from normality. In this thesis we show that the optimal unbiased estimating equation coincides with the likelihood equations for normal data. We then introduce a general class of weighted unbiased estimating equations to estimate parameters in a structured correlation matrix. We derive expressions for asymptotic covariance of the estimates, …

Statistical Analysis Of Longitudinal And Multivariate Discrete Data, Deepak Mav

Mathematics & Statistics Theses & Dissertations

Correlated multivariate Poisson and binary variables occur naturally in medical, biological and epidemiological longitudinal studies. Modeling and simulating such variables is difficult because the correlations are restricted by the marginal means via Fréchet bounds in a complicated way. In this dissertation we will first discuss partially specified models and methods for estimating the regression and correlation parameters. We derive the asymptotic distributions of these parameter estimates. Using simulations based on extensions of the algorithm due to Sim (1993, Journal of Statistical Computation and Simulation, 47, pp. 1–10), we study the performance of these estimates using infeasibility, coverage probabilities of the …

A Comparison Of Esomeprazole And Lansoprazole For Control Of Intragastric Ph In Patients With Symptoms Of Gastro-Oesophageal Reflux Disease, D. A. Johnson, T. Stacy, M. Ryan, T. Wootton, J. Willia, K. Hornbuckle, W. Brooks, M. Doviak

Mathematics & Statistics Faculty Publications

Background: Intragastric acid suppression is the most direct measure of the pharmacodynamic efficacy of proton pump inhibitors, which are the most effective drugs for acid-related diseases.

Aim: To compare the effectiveness of once and twice daily dosing of lansoprazole and esomeprazole in controlling intragastric acidity ( target gastric pH > 4.0) over a 24-hour period.

Methods: In an open-label, two-way crossover study, 45 Helicobacter pylori-negative patients with gastro-oesophageal reflux disease were randomized to receive one of two regimens: 30 mg lansoprazole or esomeprazole 40 mg once daily. Intragastric pH was assessed by 24-hour pH monitoring on day 5 of each regimen. …

Symptoms Of Gastro-Oesophageal Reflux Disease And The Severity Of Obstructive Sleep Apnoea Syndrome Are Not Related In Sleep Disorders Center Patients, H.-N. Kim, R. D. Vorona, M. P. Winn, M. Doviak, D. A. Johnson, J. Catesby Ware

Mathematics & Statistics Faculty Publications

Background: Studies suggest obstructive sleep apnea syndrome (OSAS) frequently manifests in patients with gastroesophageal reflux disease (GERD) and that there may be a causal relationship.

Aim: To determine the relationship between OSAS and symptoms of GERD.

Methods: Consecutive patients referred to the Sleep Disorders Center (SDC) 18 years and older with polysomnographically defined OSAS were evaluated prospectively for GERD using a validated symptoms questionnaire. The GERD and OSAS relationship was assessed by 1) determining frequency of GERD in patients with and without OSAS; 2) ascertaining the relationship between OSAS severity categories and presence of GERD; 3) examining GERD score in …

Bottleneck Analysis Of Cports, Sreekalyana Chakravarthy Kajuluri

Electrical & Computer Engineering Theses & Dissertations

CPortS is a transportation logistics simulation that models the flow of military cargo through a seaport and the interaction of the cargo with the port resources and infrastructure. It provides information about the seaport's capabilities, how the cargo has been handled, how many days the cargo took to clear a particular port area, and the overall throughput of the seaport. The model is highly data intensive since it models the huge traffic in a real seaport.

Bottlenecks reduce system performance. Systems that are traffic intensive or simulations of systems, which are data intensive, encounter bottlenecks, which reduce their performance. In …

Wishartness And Independence Of Matrix Quadratic Forms For Kronecker Product Covariance Structures, Akhil K. Vaish, N. Rao Chaganty

Mathematics & Statistics Faculty Publications

Let X be distributed as matrix normal with mean M and covariance matrix W⊗V, where W and V are nonnegative definite (nnd) matrices. In this paper we present a simple version of the Cochran’s theorem for matrix quadratic forms in X. The theorem is used to characterize the class of nnd matrices W such that the matrix quadratic forms that occur in multivariate analysis of variance are independent and Wishart except for a scale factor. © 2003 Elsevier Inc. All rights reserved.

Estimation Of Parameters In Replicated Time Series Regression Models, Genming Shi

Mathematics & Statistics Theses & Dissertations

The time series regression model was widely studied in the literature by several authors. However, statistical analysis of replicated time series regression models has received little attention. In this thesis, we study the application of quasi-least squares, a relatively new method, to estimate the parameters in replicated time series models with general ARMA( p, q) correlation structure. We also study several established methods for estimating the parameters in those models, including the maximum likelihood, method of moments, and the GEE method. Asymptotic comparisons of the methods are made bV fixing the number of repeated measurements in each series, and …

Analysis Of Multivariate Data Using Kotz Type Distribution, Kusaya Plungpongpun

Mathematics & Statistics Theses & Dissertations

Most of the inferential statistical methods for multivariate data are developed under the fundamental assumption that the data are from a multivariate normal distribution. Unfortunately, one can never be sure a set of data is really from a multivariate normal distribution. There are numerous methods for checking (testing) multivariate normality, but based on many published and our own simulation studies, provided in the first chapter of this dissertation, we observe that these tests are generally not very powerful, especially for smaller sample sizes. Hence it is always beneficial to have alternative multivariate distributions available along with the methodology for using …

Geographic Variation In The Morphology Of Crotalus Horridus (Serpentes: Viperidae), John Robert Allsteadt

Biological Sciences Theses & Dissertations

The Timber Rattlesnake (Crotalus horridus) occurs in discontinuous populations throughout the eastern and central United States. The species exhibits high levels of polymorphism in morphological traits, especially in coloration and pattern. Previous studies recognized either distinct northern and southern subspecies or three regional morphs (northern, southern, and western), but conflicting data sets and limited geographic sampling of previous studies have left the relationships among those regional variants unclear. In this study, univariate and multivariate statistics, together with a geographic information system, were used to analyze geographic variation in 36 morphological characters recorded from 2,420 specimens of C. horridus …

A Combinatorial Technique For Face Detection Based On Color And Statistical Analysis, Harishwaran Hariharan

Electrical & Computer Engineering Theses & Dissertations

Automatic detection of faces from video sequences is an important task in security applications. The number, location, size and orientation of human faces in a video frame are unpredictable and can vary from frame to frame. A face detection algorithm for color images in the presence of varying lighting conditions and complexity in background relying upon color and statistical analysis is presented in this thesis. The new method detects skin regions over the entire image and then classifies the skin regions as faces and non-faces. Segmentation of skin regions is performed by a novel color space merging procedure named Integrated …

Support For Statistical Analysis Of The Configurable Port Simulation (Cports), Saurav Mazumdar

Electrical & Computer Engineering Theses & Dissertations

The primary objective of this thesis is to provide support for statistical analysis of CPortS: a transportation logistics simulation, which models the movement of military traffic through seaports and the interaction of the traffic with port infrastructure. By any standards, CPortS is a very large, data intensive simulation. It provides capabilities for analyzing many important issues such as port clearance and throughput. CPortS was classically run in single run mode. Only a single replication of the simulation was performed and conclusions were drawn from the results obtained. Users and analysts of CPortS performed multiple runs only to see the effect …

Nearly Balanced And Resolvable Block Designs, Brian Henry Reck

Mathematics & Statistics Theses & Dissertations

One of the fundamental principles of experimental design is the separation of heterogeneous experimental units into subsets of more homogeneous units or blocks in order to isolate identifiable, unwanted, but unavoidable, variation in measurements made from the units. Given v treatments to compare, and having available b blocks of k experimental units each, the thoughtful statistician asks, “What is the optimal allocation of the treatments to the units?” This is the basic block design problem. Let n_ij be the number of times treatment i is used in block j and let N be the v x b matrix N …

Mark-Recapture Creel Survey And Survival Models, Shampa Saha

Mathematics & Statistics Theses & Dissertations

In this dissertation, we consider a model based approach to the estimation of exploitation rate of a fish population by combining mark-recapture procedures with a creel survey. We also consider the analysis of a proportional hazards survival model for randomly censored observations, known as the Koziol-Green model. The model assumes that the lifetime survivor function is a power of the censored time survivor function.

In Chapter 2, we introduce the model based approach to the estimation of the exploitation rate of a fish population by combining mark-recapture procedures with a creel survey. We assume that in the beginning of a …

Single Row Routing: Theoretical And Experimental Performance Evaluation, And New Heuristic Development, David A. Hysom

Computer Science Theses & Dissertations

The Single Row Routing Problem (SRRP) is an abstraction arising from real-world multilayer routing concerns. While NP-Complete, development of efficient SRRP routing heuristics are of vital concern to VLSI design. Previously, researchers have introduced various heuristics for SRRP; however, a comprehensive examination of SRRP behavior has been lacking.

We are particularly concerned with the street-congestion minimization constraint, which is agreed to be the constraint of greatest interest to industry. Several theorems stating lower bounds on street congestion are known. We show that these bounds are not tight in general, and argue they may be in error by at least 50% …

Analysis Of Repeated Measures Data Under Circular Covariance, Andrew Montgomery Hartley

Mathematics & Statistics Theses & Dissertations

Circular covariance is important in modelling phenomena in epidemiological, communications and numerous physical contexts. We introduce and develop a variety of methods which make it a more versatile tool. First, we present two classes of estimators for use in the presence of missing observations. Using simulations, we show that the mean squared errors of the estimators of one of these classes are smaller than those of the Maximum Likelihood (ML) estimators under certain conditions. Next, we propose and discuss a parsimonious, autoregressive type of circular covariance structure which involves only two parameters. We specify ML and other types of estimators …

Optimality And Construction Of Designs With Generalized Group Divisible Structure, Sudesh K. Srivastav

Mathematics & Statistics Theses & Dissertations

This thesis is an investigation of the optimality and construction problems attendant to the assignment of v treatments to experimental units in b blocks of size k, paying special attention to settings for which equal replication of the treatments is not possible. The model is that of one way elimination of heterogeneity, in which the expectation of an observation on treatment i in block j is T_i + βj (treatment effect + block effect), where T_i and βj are unknown constants, 1 ≤ i ≤ v and 1 ≤ j ≤ b. All observations are assumed to …

Linear Models For Multivariate Repeated Measures Data, Shantha S. Rao

Mathematics & Statistics Theses & Dissertations

In this dissertation we focus mainly on the analysis of continuous multivariate repeated measurements data based on the assumption of multivariate normality. However certain aspects of the analysis of univariate repeated measures data are also considered. Typically, we have measurements on p variables (possibly correlated) in the form of px1 vectors y_ijk observed at k = 1,2, ...,t_ij occasions on j = 1,2, ..., n_i individuals from i = 1,2, ..., g groups. We assume a naturally occurring covariance structure V_ij ⊗ ∑ among the p variables on the j^th individual from i^th group …

Adaptive Integration Of Audio And Visual Information Using Discrete And Semi-Continuous Hidden Markov Models In Audiovisual Automatic Speech Recognition, Qin Su

Electrical & Computer Engineering Theses & Dissertations

An audiovisual semi-continuous hidden Markov model (HMM)-based Automatic Speech Recognition (ASR) system and an improved method of integrating audio and visual information in an audiovisual discrete HMM-based ASR system are investigated.

In the audiovisual discrete HMM, an adaptive integration formulation is employed, which incorporates the integration into the HMM at a pre-categorical stage. A visual weighting parameter is determined automatically, which allows the relative contribution of audio and visual information to be adjusted adaptively. Using an adaptive weight, the accuracy increased by 13% compared to the same model with no adaptive weight.

The semi-continuous HMM is a class of models …

Analysis Of Growth Curves Under Some Special Covariance Structures, Shobha Prabhala

Mathematics & Statistics Theses & Dissertations

In this dissertation we consider the growth curve or generalized MANOVA model in its most general form given by and develop statistical methodology for analyzing data using this model. Here g represents the number of groups, Y_ij is the observation matrix, ξ is a matrix of unknown parameters, A_i is a known matrix of rank g, and B_ij is a matrix of rank k. Further, the rows of the error matrix ∈_ij are independent and each distributed as N_pij (0, Σ_ij).This model accommodates different kinds of unbalanced data, such as, monotone data, data …

Predicting Utility Bills For Air Combat Command A Study Of Forecasting Techniques, William L. Luthie

Engineering Management & Systems Engineering Theses & Dissertations

Many companies use forecasting techniques as a tool in managing their assets. Trends in such items as sales, population and inventory levels have all been determined at one time or another using forecasting, yet research indicates that these tools have not been utilized to predict utility budgets. This research was conducted to determine if such techniques could be applied to the specific task of predicting the utility bill at an Air Force base. Three quantitative models were chosen, the Moving Average, Exponential Smoothing and Regression, to determine their applicability to the task at hand. One base within Air Combat Command, …

Comparing Traditional Statistical Models With Neural Network Models: The Case Of The Relation Of Human Performance Factors To The Outcomes Of Military Combat, William Oliver Hedgepeth

Engineering Management & Systems Engineering Theses & Dissertations

Statistics and neural networks are analytical methods used to learn about observed experience. Both the statistician and neural network researcher develop and analyze data sets, draw relevant conclusions, and validate the conclusions. They also share in the challenge of creating accurate predictions of future events with noisy data.

Both analytical methods are investigated. This is accomplished by examining the veridicality of both with real system data. The real system used in this project is a database of 400 years of historical military combat. The relationships among the variables represented in this database are recognized as being hypercomplex and nonlinear.

The …

Some Sampling Designs And Estimation Problems, Hassan Lakkis

Mathematics & Statistics Theses & Dissertations

In the first chapter we review some standard estimators in sampling from a finite population, and some design-based estimators in sampling from a continuous universe.

In concert with the theory initiated by professor Douglas Robson (personal communication) and later presented by Cordy (1993), we consider design-based variance estimation for probability sampling from a continuous and spatially distributed universe. Using this theory in chapter two, the sampling design of one random point from each cell of a translated grid is investigated and the problem of edge effects on estimation is illustrated with examples. Also in chapter four, standard systematic sampling methods …

Methods For The Comparison Of Timing Behavior Applied To The Pink Salmon Fisheries Of Prince William Sound, Alaska, Louis J. Rugolo

OES Theses and Dissertations

Harvest control in salmonid fisheries was examined as a problem in the formulation of regulations which restrict time and area of fishing. An ability to rigorously define and compare the form of the progression of migration across time and between harvest areas was judged fundamental to objective harvest decisions. Identification and evaluation of statistical methods appropriate to the comparison of empirical migratory time densities was performed.

The development of the measure of central tendency (mean date) of the time density as the consistent, unbiased estimator of migratory behavior was given. Practical evidence demonstrated that the mean date was highly resistant …

Invariance Properties Of Statistical Tests For Dependent Observations, Akhil K. Vaish

Mathematics & Statistics Theses & Dissertations

In this dissertation we assume that the observations are from normal populations but are correlated and study the problem of characterizing the class of covariance structures such that the distributions of the popular test statistics remain invariant, that is, they remain the same except for a constant factor. We first obtain some simple extensions and variations of the well known Cauchy-Schwarz inequality. Incidentally, several inequalities that are useful in the detection of outliers can be deduced from our results.

Our main result is a characterization of the class of all nonnegative definite solutions W to the matrix equation AWA = …

Impact Of Field-Dependent Electronic Trapping Across Coulomb Repulsive Potentials On Low Frequency Charge Oscillations, R. P. Joshi, K. H. Schoenbach, P. K. Raha

Bioelectrics Publications

We have performed Monte Carlo simulations to obtain the field dependence of electronic trapping across repulsive potentials in GaAs. Such repulsive centers are associated with deep level impurities having multiply charged states. Our results reveal a field‐dependent maxima in the electronic capture coefficient, and the overall shape is seen to depend on the background electron density due to the effects of screening. Based on the Monte Carlo calculations, we have examined the stability of compensated semiconductors containing such repulsive centers. Our analysis indicates a potential for low frequency charge oscillations which is in keeping with available experimental data.

Studies Of Electron-Beam Penetration And Free-Carrier Generation In Diamond Films, R. P. Joshi, K. H. Schoenbach, C. Molina, W. W. Hofer

Bioelectrics Publications

Experimental observations of the energy‐dependent electron‐beam penetration in type II‐A natural diamond are reported. The experimental data are compared with results obtained from numerical Monte Carlo simulations, and the results are in very good agreement. The results also reveal that a threshold energy of about 125 keV is necessary for complete penetration for a 35 μm sample. It is found that over the 30–180 keV range, the energy dependence of the penetration depth and total path length exhibits a power‐law relation. Monte Carlo simulations have also been performed to investigate the excess carrier‐generation profiles within diamond for a set of …

The Use Of A Factory Simulation To Evaluate A Flexible Control Structure For Integrated Manufacturing, Ling Ling Pan

Engineering Management & Systems Engineering Theses & Dissertations

Once a control structure for an integrated manufacturing system is decided upon, manufacturing activities are limited by that structure. A flexible control structure is presented as an approach for accommodating a variety of manufacturing activities, without being limited to a single control structure. A flexible control structure is one that allows multiple types of control structure in the manufacturing process. For example, both hierarchical and non-hierarchical structures may be used in a flexible structure. The properties of a flexible control structure are discussed from the point of view of graph theory.

Control structures for automated manufacturing are difficult to evaluate …

Multidimensional Approach To Implementation Of Continuous Process Improvement Utilizing Small Run Analysis In A Shipyard Environment, Paul Ray Hollandsworth

Engineering Management & Systems Engineering Theses & Dissertations

Nationally, both public and private shipyards are experiencing a high rework rate (over 40%) in the fabrication of plug connectors used for electronic systems onboard Navy vessels. The shipyard's survival depends on acquiring the elements necessary to maintain a major industry in a position of continuous improvement that produces a better product than their competitors, at less cost, in a safe manner, and on schedule.

This research addresses the complex problem of how to introduce quality control methodologies within a job shop environment that assists in identifying variables that influence the rework rate of plug fabrication process over a four …