Statistics and Probability Commons^™

A New Test For The Mean Vector In High Dimensional Setting, Behzad Aalipur Hafshejani

Open Access Theses & Dissertations

Traditional statistical data analysis mostly includes methods and techniques to deal with problems in which there are many observations but a few variables. Nonetheless, the current inclination is toward more observations but also, toward more variables. Today's observations gathered on individuals are images, curves, or even movies. Unfortunately many traditional methods do not work well in high dimensional settings. As an example Hotelling's test which is well known and widely used in the literature does not work when it comes to high dimensional problems. Consequently statisticians are making an effort to find remedies or new approaches to multivariate mean testing. …

Sample Size Estimation For Genomics Experiments With Dependent End Points, Desmond Koomson

Open Access Theses & Dissertations

In typical genomics studies involving numerous association tests of gene mutations with a disease, error rate control via multiplicity adjustment is paramount because even if all genes were to be non-differentially associated, we would still make some false positives. Many methods exist that incorporate the control of multiplicity for normally distributed endpoints in sample size estimation, but none addresses the issue for non-normally correlated endpoints.

One common practice in the literature is to assume an equal correlation among all differentially associated or expressed genes, thereby using the generalized binomial or beta-binomial model to compute the comparison-wise power of detecting these …

On Six-Parameter Fréchet Distribution: Properties And Applications, Haitham M. Yousof, Ahmed Z. Afify, Abd El Hadi N. Ebraheim, Gholamhossein G. Hamedani, Nadeem Shafique Butt

Mathematics, Statistics and Computer Science Faculty Research and Publications

This paper introduces a new generalization of the transmuted Marshall-Olkin Fréchet distribution of Afify et al. (2015), using Kumaraswamy generalized family. The new model is referred to as Kumaraswamy transmuted Marshall-Olkin Fréchet distribution. This model contains sixty two sub-models as special cases such as the Kumaraswamy transmuted Fréchet, Kumaraswamy transmuted Marshall-Olkin, generalized inverse Weibull and Kumaraswamy Gumbel type II distributions, among others. Various mathematical properties of the proposed distribution including closed forms for ordinary and incomplete moments, quantile and generating functions and Rényi and η-entropies are derived. The unknown parameters of the new distribution are estimated using the maximum …

Certain Characterizations Of Recently Introduced Distributions, Gholamhossein G. Hamedani, Seyed Morteza Najibi

Mathematics, Statistics and Computer Science Faculty Research and Publications

Various characterizations of twenty two recently introduced distributions are presented. These characterizations are based on: (I) ration of two truncated moments; (ii) the hazard function and (iii) conditional expectations.

A New Weibull-G Family Of Distributions, M. H. Tahir, Muhammad Zubair, M. Mansoor, Gauss M. Cordeiro, Morad Alizadeh, Gholamhossein Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

Statistical analysis of lifetime data is an important topic in reliability engineering, biomedical and social sciences and others. We introduce a new generator based on the Weibull random variable called the new Weibull-G family. We study some of its mathematical properties. Its density function can be symmetrical, left-skewed, right-skewed, bathtub and reversed-J shaped, and has increasing, decreasing, bathtub, upside-down bathtub, J, reversed-J and S shaped hazard rates. Some special models are presented. We obtain explicit expressions for the ordinary and incomplete moments, quantile and generating functions, Renyi entropy, order statistics and reliability. Three useful characterizations based on truncated moments are …

Worldwide Cutaneous Malignant Melanoma Incidences Analyzed By Sex, Age, And Skin Type Over Time (1955–2007): Is Hpv Infection Of Androgenic Hair Follicular Melanocytes A Risk Factor For Developing Melanoma Exclusively In People Of European-Ancestry?, Stephen Merrill, Madhan Subramanian, Dianne E. Godar

Mathematics, Statistics and Computer Science Faculty Research and Publications

The cutaneous malignant melanoma (CMM) incidence has been increasing in an exponential manner in certain populations around the world for over 7 decades. To help illuminate the etiology, we performed worldwide temporal (1955–2007) CMM incidence analysis by sex, age (0–14, 15–29, 30–49, 50–69, 70–85+), and skin type on 6 continents using data from the International Agency for Research on Cancer. We observe an exponential increase in the CMM incidence over time and an increase of about 2 orders of magnitude between age groups 0–14 and 15–29 exclusively in European-ancestry populations around the world independent of skin type (I–III or III–IV). …

Cohomology Operations On Random Spaces, Matthew John Zabka

Wayne State University Dissertations

Topology has recently received more attention from statisticians as some its tools have been applied to understanding the shape of data. In particular, a data set can generate a topological space, and this space’s topological structure can give us insight into some properties of the data. This framework has made it necessary to study random spaces generated by data. For example, without an understanding of the probabilistic properties of random spaces, one cannot conclude with any degree of confidence what the tools of topology tell us about a data set. While some results are known about the cohomological structure of …

Salvage Brachytherapy For Biochemically Recurrent Prostate Cancer Following Primary Brachytherapy, John M. Lacy, William A. Wilson, Raevti Bole, Li Chen, Ali S. Meigooni, Randall G. Rowland, William H. St. Clair

Urology Faculty Publications

Purpose. In this study, we evaluated our experience with salvage brachytherapy after discovery of biochemical recurrence after a prior brachytherapy procedure. Methods and Materials. From 2001 through 2012 twenty-one patients treated by brachytherapy within University of Kentucky or from outside centers developed biochemical failure and had no evidence of metastases. Computed tomography (CT) scans were evaluated; patients who had an underseeded portion of their prostate were considered for reimplantation. Results. The majority of the patients in this study (61.9%) were low risk and median presalvage PSA was 3.49 (range 17.41–1.68). Mean follow-up was 61 months. At last follow-up after reseeding, …

Causal Inference In Observational Studies With Clustered Data, Meng Wu

Legacy Theses & Dissertations (2009 - 2024)

In this thesis, we study causal inference in observational studies with clustered data.

Estimating Survival Distributions, Important Covariates And Time-Varying Associations, Yan Wu

Legacy Theses & Dissertations (2009 - 2024)

There are three papers each on a different topic in this thesis. The first paper proposes a new objective methodology to estimate any subject specific survival distribution with potential time-varying effect by adjusting approximated polynomial censored survival function with estimated censoring distribution under three different assumptions: uniform censoring, independent censoring and non-informative censoring. The coefficients of the polynomial censored survival function and underlying censoring probability are estimated at each event or censoring time point across the study time frame, which naturally accommodates potential non-proportional hazards along with time-varying effect. An extensive simulation study indicates that the proposed methods usually perform …

Collective Action And Decision Making: An Analysis Of Economic Modeling And Environmental Free-Riding, Thomas Miller 16

Honor Scholar Theses

No abstract provided.

The Smallest Non-Autograph, Benjamin Baumer, Yijin Wei, Gary S. Bloom

Mathematics Sciences: Faculty Publications

Suppose that G is a simple, vertex-labeled graph and that S is a multiset. Then if there exists a one-to-one mapping between the elements of S and the vertices of G, such that edges in G exist if and only if the absolute difference of the corresponding vertex labels exist in S, then G is an autograph, and S is a signature for G. While it is known that many common families of graphs are autographs, and that infinitely many graphs are not autographs, a non-autograph has never been exhibited. In this paper, we identify the smallest non-autograph: a graph …

On Variable Bandwidth Kernel Density And Regression Estimation, Janet Nakarmi

Electronic Theses and Dissertations

We study the ideal variable bandwidth kernel density estimator introduced by McKay (1993) and the plug-in practical version of the variable bandwidth kernel density estimator with two sequences of bandwidths as in Ginè and Sang (2013).We estimate the variance of the variable bandwidth kernel density estimator. Based on the exact formula of the bias and the variance of the variable bandwidth kernel density estimator, we develop the optimal bandwidth selection of the true variable bandwidth kernel density estimator. Furthermore, we present the central limit theorem of the true variable bandwidth kernel density estimator. We also propose a new variable bandwidth …

Semi-Parametrics Dose Finding Methods, Matthieu Clertant, John O'Quigley

COBRA Preprint Series

We describe a new class of dose finding methods to be used in early phase clinical trials. Under some added parametric conditions the class reduces to the family of continual reassessment method (CRM) designs. Under some relaxation of the underlying structure the method is equivalent to the CCD, mTPI or BOIN classes of designs. These latter designs are non-parametric in nature whereas the CRM class can be viewed as being strongly parametric. The proposed class is characterized as being semi-parametric since it corresponds to CRM with a nuisance parameter. Performance is good, matching that of the CRM class and improving …

Consensus Regularized Selection Based Prediction, Ping Wang

Wayne State University Theses

Integrating regularization methods within a regression framework has become a popular choice for researchers to build predictive models with lower variance and better generalization. Regularizers also aid in building interpretable models with high-dimensional data which makes them very appealing. Regularizers in general are unique in nature as they cater to data specific features such as correlation, structured sparsity, and temporal smoothness. The problem of obtaining a consensus among such diverse regularizers is extremely important in order to determine the optimal regularizer for the model. This is called the consensus regularization problem which has not received much attention in the literature, …

Development In Normal Mixture And Mixture Of Experts Modeling, Meng Qi

Theses and Dissertations--Statistics

In this dissertation, first we consider the problem of testing homogeneity and order in a contaminated normal model, when the data is correlated under some known covariance structure. To address this problem, we developed a moment based homogeneity and order test, and design weights for test statistics to increase power for homogeneity test. We applied our test to microarray about Down’s syndrome. This dissertation also studies a singular Bayesian information criterion (sBIC) for a bivariate hierarchical mixture model with varying weights, and develops a new data dependent information criterion (sFLIC).We apply our model and criteria to birth- weight and gestational …

Multi-State Models With Missing Covariates, Wenjie Lou

Theses and Dissertations--Statistics

Multi-state models have been widely used to analyze longitudinal event history data obtained in medical studies. The tools and methods developed recently in this area require the complete observed datasets. While, in many applications measurements on certain components of the covariate vector are missing on some study subjects. In this dissertation, several likelihood-based methodologies were proposed to deal with datasets with different types of missing covariates efficiently when applying multi-state models.

Firstly, a maximum observed data likelihood method was proposed when the data has a univariate missing pattern and the missing covariate is a categorical variable. The construction of the …

Statistical Methods For Handling Intentional Inaccurate Responders, Kristen J. Mcquerry

Theses and Dissertations--Statistics

In self-report data, participants who provide incorrect responses are known as intentional inaccurate responders. This dissertation provides statistical analyses for address intentional inaccurate responses in the data.

Previous work with adolescent self-report, labeled survey participants who intentionally provide inaccurate answers as mischievous responders. This phenomenon also occurs in clinical research. For example, pregnant women who smoke may report that they are nonsmokers. Our advantage is that we do not solely have self-report answers and can verify responses with lab values. Currently, there is no clear method for handling these intentional inaccurate respondents when it comes to making statistical inferences.

We …

Topics In Logistic Regression Analysis, Zhiheng Xie

Theses and Dissertations--Statistics

Discrete-time Markov chains have been used to analyze the transition of subjects from intact cognition to dementia with mild cognitive impairment and global impairment as intervening transient states, and death as competing risk. A multinomial logistic regression model is used to estimate the probability distribution in each row of the one-step transition matrix that correspond to the transient states. We investigate some goodness of fit tests for a multinomial distribution with covariates to assess the fit of this model to the data. We propose a modified chi-square test statistic and a score test statistic for the multinomial assumption in each …

Developing An Alternative Way To Analyze Nanostring Data, Shu Shen

Theses and Dissertations--Statistics

Nanostring technology provides a new method to measure gene expressions. It's more sensitive than microarrays and able to do more gene measurements than RT-PCR with similar sensitivity. This system produces counts for each target gene and tabulates them. Counts can be normalized by using an Excel macro or nSolver before analysis. Both methods rely on data normalization prior to statistical analysis to identify differentially expressed genes. Alternatively, we propose to model gene expressions as a function of positive controls and reference gene measurements. Simulations and examples are used to compare this model with Nanostring normalization methods. The results show that …

Statistical Inference On Dynamical Systems, Hongyuan Wang

Theses and Dissertations--Statistics

The ordinary differential equation (ODE) is one representative and popular tool in modeling dynamical systems, which are widely implemented in physics, biology, economics, chemistry and biomedical sciences, etc. Because of the importance of dynamical systems in scientific studies, they are the main focuses of my dissertation.

The first chapter of the dissertation is introduction and literature review, which mainly focuses on numerical integration algorithms of ODEs that are difficult to solve analytically, as well as derivative-free optimization algorithms for the so-called inverse problem.

The second chapter is on the estimation method based on numerical solvers of differential equations. We start …

Statistical Methods For Environmental Exposure Data Subject To Detection Limits, Yuchen Yang

Theses and Dissertations--Statistics

In this dissertation, we develop unified and efficient nonparametric statistical methods for estimating and comparing environmental exposure distributions in presence of detection limits. In the first part, we propose a kernel-smoothed nonparametric estimator for the exposure distribution without imposing any independence assumption between the exposure level and detection limit. We show that the proposed estimator is consistent and asymptotically normal. Simulation studies demonstrate that the proposed estimator performs well in practical situations. A colon cancer study is provided for illustration. In the second part, we develop a class of test statistics to compare exposure distributions between two groups by using …

Statistical Inference On Trimmed Means, Lorenz Curves, And Partial Area Under Roc Curves By Empirical Likelihood Method, Yumin Zhao

Theses and Dissertations--Statistics

Traditionally the inference on trimmed means, Lorenz Curves, and partial AUC (pAUC) under ROC curves have been done based on the asymptotic normality of the statistics. Based on the theory of empirical likelihood, in this dissertation we developed novel methods to do statistical inferences on trimmed means, Lorenz curves, and pAUC. A common characteristic among trimmed means, Lorenz curves, and pAUC is that their inferences are not based on the whole set of samples. Qin and Tsao (2002), Qin et al. (2013), and Qin et al. (2011) recently published their re- searches on the inferences of trimmed means, Lorenz curves, …

Improved Models For Differential Analysis For Genomic Data, Hong Wang

Theses and Dissertations--Statistics

This paper intend to develop novel statistical methods to improve genomic data analysis, especially for differential analysis. We considered two different data type: NanoString nCounter data and somatic mutation data. For NanoString nCounter data, we develop a novel differential expression detection method. The method considers a generalized linear model of the negative binomial family to characterize count data and allows for multi-factor design. Data normalization is incorporated in the model framework through data normalization parameters, which are estimated from control genes embedded in the nCounter system. For somatic mutation data, we develop beta-binomial model-based approaches to identify highly or lowly …

Evaluating A Bystander Intervention Program On Reproductive Coercion: Using Quasi-Experimental Design Strategies To Address Methodologic Issues In Randomized Community Prevention Trials, Catherine P. Starnes

Theses and Dissertations--Epidemiology and Biostatistics

Community (or cluster) randomized trials are trials in which communities or groups of individuals (clusters) are randomized to receive the intervention of interest. Community randomized trials frequently more closely resemble a natural experiment than a randomized controlled trial (RCT) following intervention allocation. In particular, the effects of non-compliance can pose methodologic challenges in estimating the intervention effect which may require a quasiexperimental approach in order to minimize bias.

The motivating example to illustrate these issues is the Green Dot High School (GDHS) study. The GDHS study was a longitudinal, cluster-randomized controlled trial designed to assess the effectiveness of a bystander …

Existence Of Periodic Solutions For A Quantum Volterra Equation, Muhammad Islam, Jeffrey T. Neugebauer

Mathematics Faculty Publications

The objective of this paper is to study the periodicity properties of functions that arise in quantum calculus, which has been emerging as an important branch of mathematics due to its various applications in physics and other related fields. The paper has two components. First, a relation between two existing periodicity notions is established. Second, the existence of periodic solutions of a q-Volterra integral equation, which is a general integral form of a first order q-difference equation, is obtained. At the end, some examples are provided. These examples show the effectiveness of the relation between the two periodicity notions that …

Positive Solutions For A Singular Fourth Order Nonlocal Boundary Value Problem, John M. Davis, Paul W. Eloe, John R. Graef, Johnny Henderson

Mathematics Faculty Publications

Positive solutions are obtained for the fourth order nonlocal boundary value problem, u⁽⁴⁾=f(x,u), 0 < x < 1, u(0) = u''(0) = u'(1) = u''(1) - u''(2/3)=0, where f(x,u) is singular at x = 0, x=1, y=0, and may be singular at y=∞. The solutions are shown to exist at fixed points for an operator that is decreasing with respect to a cone.

Almost Automorphic Solutions Of Delayed Neutral Dynamic Systems On Hybrid Domains, Murat Adıvar, Halis Can Koyuncuoğlu, Youssef Raffoul

Mathematics Faculty Publications

We study the existence of almost automorphic solutions of the delayed neutral dynamic system on hybrid domains that are additively periodic. We use exponential dichotomy and prove uniqueness of projector of exponential dichotomy to obtain some limit results leading to sufficient conditions for existence of almost automorphic solutions to neutral system. Unlike the existing literature we prove our existence results without assuming boundedness of the coefficient matrices in the system. Hence, we significantly improve the results in the existing literature. Finally, we also provide an existence result for an almost periodic solutions of the system.

Stochastic Models Of Evidence Accumulation In Changing Environments, Alan Veliz-Cuba, Zachary P. Kilpatrick, Krešimir Josić

Mathematics Faculty Publications

Organisms and ecological groups accumulate evidence to make decisions. Classic experiments and theoretical studies have explored this process when the correct choice is fixed during each trial. However, we live in a constantly changing world. What effect does such impermanence have on classical results about decision making? To address this question we use sequential analysis to derive a tractable model of evidence accumulation when the correct option changes in time. Our analysis shows that ideal observers discount prior evidence at a rate determined by the volatility of the environment, and the dynamics of evidence accumulation is governed by the information …

Necessary And Sufficient Conditions For Stability Of Volterra Integro-Dynamic Equation Systems On Time Scales, Youssef Raffoul

Mathematics Faculty Publications

In this research we establish necessary and sufficient conditions for the stability of the zero solution of scalar Volterra integro-dynamic equation on general time scales. Our approach is based on the construction of suitable Lyapunov functionals. We will compare our findings with known results and provides application to quantum calculus.