Statistics and Probability Commons^™

Why Copulas?, Vladik Kreinovich, Hung T. Nguyen, Songsak Sriboonchitta, Olga Kosheleva

Departmental Technical Reports (CS)

A natural way to represent a 1-D probability distribution is to store its cumulative distribution function (cdf) F(x) = Prob(X ≤ x). When several random variables X₁, ..., X_n are independent, the corresponding cdfs F₁(x₁), ..., F_n(x_n) provide a complete description of their joint distribution. In practice, there is usually some dependence between the variables, so, in addition to the marginals F_i(x_i), we also need to provide an additional information about the joint distribution of the given variables. It is possible to represent this joint …

Bayesian Adaptive Penalized Splines In Nonparametric Regression And In Spectral Time Series Analysis, Luis Angel Mora

Open Access Theses & Dissertations

A Bayesian approach to nonparametric regression using Penalized splines (P-splines) is presented. The approach uses the linear mixed model formulation of P-spines. The usual model assumes a single value for the smoothing parameter controlling the amount of smoothing of the fitted function. The main focus of the Thesis is on spatially adaptive smoothing where the smoothing parameter is a function of the covariate so that different amounts of smoothing are applied in different regions of the covariate. An application to spectral time series analysis will be demonstrated. Markov chain Monte Carlo methods are used to make inference based on the …

Combining Semiparametric Regression And Kriging For Prediction Of Pm2.5 Pollutant Levels At Unmonitored Locations With Meterological And Traffic Data, Justin Jonathan Strate

Open Access Theses & Dissertations

Particulate matter (PM) is defined by the Texas Commission on Environmental Quality (TCEQ) as "a mixture of solid particles and liquid droplets found in the air". These particles vary widely in size. Those particles that are less than 2.5 micrometers in aerodynamic diameter are known as Particulate Matter 2.5 or PM2.5. These particles are inhaled, and their health effects are still largely being studied. Past studies have assessed PM2.5 exposure of a population, yet individual exposure is more diffcult to assess and may vary widely in a population. Recent studies have combined semiparametric models with kriging (Li et. al [2012]) …

A Bayes Approach In Step-Stress Accelerated Life Testings, Hao Yang Teng

Open Access Theses & Dissertations

A Bayesian analysis for the Weibull proportional hazard (PH) model is presented. A comparison between the Weibull PH model and the Weibull cumulative exposure (CE) model is made graphically and mathematically. The PH model is as flexible as the CE model in fitting step-stress data and the mathematical form of the PH model enables researchers to do Bayesian inferencemuch easier than the CE model. In addition, the PH model has the desirable proportional hazard property. A convex tent prior is used for Bayesian analysis. Markov chain Monte Carlo methods are used for posterior inferences. In this study, we adopt two …

Pre-Tuned Ridge Regression And Its Extension To Generalized Linear Models, Yaa Tawiah Wonkye

Open Access Theses & Dissertations

Ridge regression is regularization or shrinkage method and a common approach in dealing with multicollinearity in conventional regression analysis. Ridge regression is widely used by statistical analyst since it is one of the best compared to other regularization methods. Also, the introduction of high dimension and ultra-high dimensional data has become an issue of concern and ridge regression is one way of dealing with such data. One of the key issues associated with ridge regression is the determination of the tuning or ridge parameter. The common practice is to fit ridge regression for a different number of values of tuning …

Towards Analytical Techniques For Optimizing Knowledge Acquisition, Processing, Propagation, And Use In Cyberinfrastructure, Leonardo Octavio Lerma

Open Access Theses & Dissertations

For many decades, there has been a continuous progress in science and engineering applications.

A large part of this progress comes from the new knowledge that researchers acquire, propagate, and use. This new knowledge has revolutionized many aspects of our life, from driving to communications to shopping.

Somewhat surprisingly, there is one area of human activity which is the least impacted by the modern technological progress: the very processes of acquiring, processing, and propagating information. When we decide where to place sensors, which algorithm to use for processing the data – we rely mostly on our own intuition and on …

Resampling-Based Multiple Comparisons For Generalized Linear Models, Josephine Sarpong Akosa

Open Access Theses & Dissertations

Diverse applications in medical and epidemiological research routinely utilize generalized linear modeling to explain the relationship between the incidence of disease and particular risk factors. Researchers' interest in such models are estimated quantities from the model such as the response probabilities, the relative risks or the odds ratios and not the model itself. Often, the simultaneous estimation of these quantities or a subset of the quantities are warranted. The results are usually reported via confidence intervals at a pre-specified level of significance. Utilizing the usual 95% pointwise confidence intervals for the simultaneous inference inflates the risk of making type I …

A New Bivariate Distribution With Applications, Sathya Amarasekara

Open Access Theses & Dissertations

We construct a bivariate distribution of (X, Y ) by assuming that the conditional distribution of Y given X is a two-parameter Gamma (s, ν(x)), where the scale parameter depends on X. If X is assumed to be any distribution, then clearly the joint distribution is well defined in all cases. We will study this new distribution by developing all possible properties, moments, shapes and estimation of parameters with a view towards applications of the distribution to data from many random number generation methods.

A Long- And Short-Run Analysis Of Electricity Demand In Ciudad Juarez, Ericka Cecilia Mendez

Open Access Theses & Dissertations

Economic growth and appliance saturation are increasing electricity consumption in Mexico. Annual frequency data from 1990 to 2012 are utilized to develop an error correction framework that sheds light on short- and long-run electricity consumption behavior in Ciudad Juarez, a large Mexican metropolitan economy at the border with the United States. The results for this study reveal that electricity is an inelastic normal good in this market. Moreover, natural gas is found to be a weak complement to electricity. With regards to the customer base in this urban economy, population, employment, and income exercise positive and statistically significant impacts on …

Variable Selection For Cox Proportional Hazards Models Via Subtle Uprooting, Chalani S. Wijayasinghe

Open Access Theses & Dissertations

Cox proportional hazards model (Cox PH model) is heavily used in survival analysis to assess the importance of various covariates on the survival times of individuals or objects through the hazard function. This study suggests a new variables selection method for Cox PH models, under the title 'Subtle uprooting', that does variable selection and model estimation for Cox proportional hazards (PH) models simultaneously.

There are subset selection methods and shrinkage selection methods suggested in the context of Cox PH model. However the subset selection methods become infeasible in higher dimensions and the available shrinkage methods need tuning of parameters making …

Comparison Of Bayesian Nonparametric Density Estimation Methods, Adel Bedoui

Open Access Theses & Dissertations

Density estimation has a long history in statistics. There are two main approaches to density, estimation parametric and nonparametric. The first approach requires specification of a family of densities f and estimation of the unknown parameter $\theta$ using a suitable estimation method, for example, maximum likelihood estimation. This approach may be prone to bias that arises from either estimation of the parameter or from incorrect specification of the probability distribution. The second approach, does not assume a specific parametric family.

In this thesis, we implement three density estimation methods that use Bayesian nonparametric approaches utilizing Markov Chain Monte Carlo methods. …

Multiplicity Adjustments For Respecification Searches In Structural Equation Models, John Appiah Kubi

Open Access Theses & Dissertations

Structural Equation Modeling (SEM), as a statistical modeling technique, is one of the most comprehensive and flexible approaches to data analysis currently available. Its use has been increasing steadily over the past few decades. Generally, it refers to a family of

techniques that employs the analysis of covariance to establish relationships among a set of variables. It allows researchers (or users) to assess the adequacy of their hypothesized models with their sample data. Often times, in assessing their models, researchers are not

only interested in the overall fit of their model but they are also interested in knowing which proposed …

A Systematic Approach To Manage Missing Data In Pavement Management Systems, Mazin M. Al-Zou'bi

Open Access Theses & Dissertations

Pavements are an important part of the highway transportation infrastructure, accounting for the largest share of the overall investment. A tremendous amount of time and money is spent each year on the construction of new pavements, as well as on the maintenance and rehabilitation of existing pavements.

Transportation agencies use pavement management systems (PMS) for their maintenance and rehabilitation planning, programming, and budgeting. PMS are used to make decisions regarding when maintenance and rehabilitation should be applied. The systems also select what type of treatment should be applied for each pavement section in the network with clear estimations of the …

Principal Differential Analysis: Incorporating Covariates Using Kernel Smoothers, Christopher Alfred Dodoo

Open Access Theses & Dissertations

Principal Differential Analysis is a statistical technique which suggests that a given set of functional data curves can be annihilated completely when an estimated linear differential

operator (LDO) is applied (Coddington & Levinson). The novelty of residuals as forcing functions is introduced in PDA.

This thesis builds on PDA with covariates by Jin et al, 2012 by dropping the assumption that the coefficients of the linear differential operator are a product of a function in t and v; the equivalent kernel is used to estimate the coefficient functions at target values. Incorporating covariates with kernel smoothers leads to two …

Analysis Of Vehicle Interactions On Interstate Highways: Discrete Choice And Linear System Approaches, Alicia Romo

Open Access Theses & Dissertations

The research in this dissertation developed statistical and linear system models to predict driving behavior according to driver attributes, vehicle characteristics, car-following dynamics and/or driving conditions. The scope of this research was limited to the interaction of two vehicles traveling in the same direction on interstate highways.

The statistical models proposed in this research investigated the contributions of the different vehicle types on the manner and likelihood of collision. Discrete choice models were used to estimate the probability of the types of collision (rear-end, angle and sideswipe) as functions of driver attributes, striking and struck vehicle types, pre-crash driving actions …

From Unbiased Numerical Estimates To Unbiased Interval Estimates, Baokun Li, Gang Xiang, Vladik Kreinovich, Panagios Moscopoulos

Departmental Technical Reports (CS)

One of the main objectives of statistics is to estimate the parameters of a probability distribution based on a sample taken from this distribution. Of course, since the sample is finite, the estimate X is, in general, different from the actual value x of the corresponding parameter. What we can require is that the corresponding estimate is unbiased, i.e., that the mean value of the difference X - x is equal to 0: E[X] = x. In some problems, unbiased estimates are not possible. We show that in some such problems, it is possible to have interval unbiased estimates, i.e., …

Light Vs. Quantum Gravity, Irving Martinez^*

COURI Symposium Abstracts, Spring 2012

No abstract provided.

Generalized Linear Latent Mixed Modeling Of Functional Independent Measures And Patient Outcomes, Maduranga Kasun Dassanayake

Open Access Theses & Dissertations

The Functional Independent Measure (FIM) is one of the most widely accepted functional assessment measures used in the rehabilitation community. Past research studies have investigated the relationship between place of discharge, admission FIM scores or FIM difference scores, and patients' characteristics and found relationships between those variables. However, most of these studies fail to account for the multi-layered multidimensionality of the FIM and the measurement error associated with the FIM items. This study utilizes Generalized Linear Latent Mixed Models (GLLAMM) and Structural Equation Models (SEM) to assess which patient characteristics are associated with FIM difference scores and the structural relationship …

Arma-Garch Model Applied To Exchange-Traded Funds, Rebecca Davis

Open Access Theses & Dissertations

In this paper, time-varying volatility of some of the leading exchange-traded funds are studied. The ARMA mean equation with GARCH errors is used to model the series correlations and the conditional heteroscadesticity in the asset

returns. The conditional distributions of the standardized residuals are assumed to be skew-generalized error distribution. The high kurtosis and fat tail of the returns, were captured in all the data by fitting an ARMA-GARCH model with the conditional distribution of, skew-generalized error distribution.

Furthermore, the sample cross-correlations of these significant exchange-traded funds and the corresponding financial indices they mimic were computed. The empirical conclusion was …

Secondary Structure Prediction Of Long Rna Sequences Based On Inversion Excursions And A Modularized Mapreduce Framework, Daniel Tesfai Yehdego

Open Access Theses & Dissertations

Ribonucleic acid (RNA) molecules and their secondary structures play important roles in many biological processes including gene expression and regulation. The genomes of many viruses are also RNA molecules. Since secondary structures are crucial for RNA functionality, computational predictions of the RNA secondary structures have been widely studied. However, the tremendous demands on computer memory and computing time for complex secondary structures limit the capability of existing thermodynamically based algorithms for structure predictions to handling only short RNA sequences with a few hundred bases. One approach to overcome this limitation is by first cutting long RNA sequences into shorter, non-overlapping …

Study Of Volatility Structures In Geophysics And Finance Using Garch Models, Francis Biney

Open Access Theses & Dissertations

This work investigates the underlying volatility processes in earthquake series, explosive series, high frequency (tick) data and financial indices. Furthermore it examines the applicability of a range of GARCH specifications for modeling volatility of these series in order to identify similarities and differences in the volatility structures. The GARCH

variants considered include the basic GARCH, IGARCH, ARFIMA (0,d,0)-GARCH and FIGARCH specifications. In all the applications the methodology provides insight into features of these series volatility.

Analysis Of Differential Item Functioning On Selected Items Assessing Conceptual Knowledge Of Descriptive Statistics For Spanish-Speaking Ell And Non-Ell College Students, Angelica Amy Monarrez Rodriguez

Open Access Theses & Dissertations

Recently, there has been growing interest in promoting conceptual understanding of statistical concepts in the classroom. The Assessment Resource Tools for Improving Statistical Thinking (ARTIST) project is a resource for maintaining and developing scales useful for measuring statistical conceptual knowledge. The focus of this study is to investigate whether items assessing conceptual knowledge of measures of center and variation from the (ARTIST) database show evidence of differential item functioning when administered to English Language Learners (ELLs). This is pertinent topic since the population of English Language Learners (ELL) in the United States has been growing rapidly in the past few …

Assessing Measurement Invariance In The Presence Of Testlets, Luis Andres Alvarado

Open Access Theses & Dissertations

Dealing with measurement invariance has been an issue of concern in confirmatory factor analysis for many years. It is important to establish measurement invariance across groups so that instruments may be validly used in multiple groups for comparison of the mean or summative scores. Throughout the years, many studies have considered testing for measurement invariance in factor models. However, there have been no studies that assess measurement invariance when so-called testlets should be modeled in the factor analytic model. Testlets add nuisance covariation to the model which can interfere when trying to detect measurement invariance. In the past, models have …

Estimating The Effect Of Dust And Low Wind Events On Hospitalizations For Asthma While Adjusting For Hourly Levels Of Air Pollutants, Priyangi Kanchana Bulathsinhala

Open Access Theses & Dissertations

El Paso, Texas is known as one of the dust hotspots in North America. We explore the effect of dust and low wind events on asthma admissions in El Paso, Texas between 2000 and 2005. Conditional logistic regression with a case-crossover design was used to estimate the probability of hospitalization after dust and low wind events while controlling for pollutants with hourly monitor measurements, and weather. The historical functional linear model is used to incorporate the hourly pollutant measures into the regression model with a continuous lag, as an alternative to a distributed lag model based on daily averages. The …

Estimating Statistical Characteristics Under Interval Uncertainty And Constraints: Mean, Variance, Covariance, And Correlation, Ali Jalal-Kamali

Open Access Theses & Dissertations

In many practical situations, we have a sample of objects of a given type. When we measure the values of a certain quantity x for these objects, we get a sequence of values x1, . . . , xn. When the sample is large enough, then the arithmetic mean E of the values xi is a good approximation for the average value of this quantity for all the objects from this class. Other expressions provide a good approximation to statistical characteristics such as variance, covariance, and correlation.

The values xi come from measurements, and measurement is never absolutely accurate.

Often, …

Computational Methods Of Hidden Markov Models With Respect To Cpg Island Prediction In Dna Sequences, Roberto Angel Ortega

Open Access Theses & Dissertations

Hidden Markov models (HMM's) are a specific case of Markov models where, contrary to Markov chains, the observer is unaware of what state the model was in when the symbol is observed. Like Markov chains, HMM's assume that the future state of a sequence is dependent only on the current state of the sequence. The parameters associated with HMM's are transition and emission probabilities, where transition probabilities are associated with the probability of transitioning from one state to another, and emission probabilities are the probabilities associated with observing a symbol given it came from a specific state.

The structure of …

Bayesian Computational Methods For Hidden Markov Models, Samson Laine Ghebremariam

Open Access Theses & Dissertations

Hidden Markov Models (HMMs) have been applied to many real-world problems. Hidden Markov modeling has recently become increasingly important and popular among researchers,and many software tools are based on them. Given that the models are rich in mathematical structure, they can form theoretical foundation for use in a wide range of applications. Hidden Markov models provide a universal configuration for statistical analysis of a large variety of DNA sequences containing symbols A, C, G, T. In a HMM, it is impossible to figure out what state the model is in by just having a look at the symbol generated.

A …

A Proposed Epithermal Model For The High Grade District, California, Michael Nicholas Feinstein

Open Access Theses & Dissertations

A historic gold mining district in northeastern California has not been incorporated into the global knowledge base for precious metal vein deposits. This study collected various data types which are important characteristics in the classification and understanding of vein deposits. The High Grade District (HGD) is a gold mining site located in the northeast corner of Modoc County, California, in the Warner Mountains. The Warner Mountains are composed of Tertiary eruptive centers, cropping out between valleys formed through extensional tectonics. Mineralization of the HGD displays abundant silicification, adularia, and gold; these characteristics are sufficient to classify mineralization as low-sulfidation epithermal …

Gamma And Generalized Gamma Distributions, Victor Hugo Jiménez Nava

Open Access Theses & Dissertations

We present the Generalized Gamma Distribution, study its properties and derive the estimators of the parameters. This distribution includes many standard forms, like: Gamma, Exponential, Weibull, Half Normal and others. Sum and ratios of independent generalized gamma lead to intractable forms. However approximation works well. In particular two-moment gamma and three moment normal approximations are shown to approximate the sum of k independent gamma as well as generalized gamma distributions.

Principal Differential Analysis With Covariates : A Simulation Study On The Effect Of The Smoothing Parameters, Indika Varuna Mallawaarachchi

Open Access Theses & Dissertations

Principal Differential Analysis deals with functional data. The word functional data refers to a collection of curves that are independent and measured on a dense grid of time points in an interval. These time points can be equally or unequally spaced. A differential equation is believed capable of capturing the features of these n curves.

Ramsay(1996) first introduced Principal Differential Analysis (PDA) as an alternative to the Principal Component Analysis(PCA). PDA finds a linear differential equation that captures features of a collection of curves, in order to have a low dimensional approximation for functional data. PDA is based on the …