Statistics and Probability Commons^™

Shrinkage Estimation In The Inverse Rayleigh Distribution, Gyan Prakash

Journal of Modern Applied Statistical Methods

The properties of the shrinkage test–estimators of the parameter were studied for an inverse Rayleigh model under the asymmetric loss function. Both the single and double–stage shrinkage test–estimators are considered.

Combining Independent Tests Of Conditional Shifted Exponential Distribution, Abedel-Qader S. Al-Masri

Journal of Modern Applied Statistical Methods

The problem of combining n independent tests as n→∞ for testing that variables are uniformly distributed over the interval (0, 1) compared to their having a conditional shifted exponential distribution with probability density function f (xθ ) = e^{−(x−γθ)} , x ≥γθ , θ ∈[a,∞), a ≥ 0 was studied. This was examined for the case where θ₁, θ₂, … are distributed according to the distribution function (DF) F and when the DF is Gamma (1, 2). Six omnibus methods were compared via the Bahadur efficiency. It is shown that, as γ → 0 and …

A Comparative Study For Bandwidth Selection In Kernel Density Estimation, Omar M. Eidous, Mohammad Abd Alrahem Shafeq Marie, Mohammed H. Baker Al-Haj Ebrahem

Journal of Modern Applied Statistical Methods

Nonparametric kernel density estimation method does not make any assumptions regarding the functional form of curves of interest; hence it allows flexible modeling of data. A crucial problem in kernel density estimation method is how to determine the bandwidth (smoothing) parameter. This article examines the most important bandwidth selection methods, in particular, least squares cross-validation, biased crossvalidation, direct plug-in, solve-the-equation rules and contrast methods. Methods are described and expressions are presented. The main practical contribution is a comparative simulation study that aims to isolate the most promising methods. The performance of each method is evaluated on the basis of the …

Time Series Models For Computing Activation In Fmri, Daniel W. Adrian, Ranjan Maitra, Daniel B. Rowe

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Shrinkage Estimation In Partially Linear Models With Measurement Error, Yifang Li

All Theses

In practice, measurement error in the covariates is often encountered. Measurement error has several effects when using ordinary least squares for the regression problems. In this thesis, we introduce the basic idea of correcting the bias caused by different types of measurement error. We then focus on the variable selection for partially linear models when some of the covariates are measured with additive errors. The bias caused by the measurement error is corrected by subtracting a bias correction term in the squared loss function. Adaptive LASSO is used for the variable selection procedure. The rate of convergence and the asymptotic …

On Robustification Of Some Procedures Used In Analysis Of Covariance, Kuanwong Watcharotone

Dissertations

This study discusses robust procedures for the analysis of covariance (ANCOVA) models. These methods are based on rank-based (R) fitting procedures, which are quite analogous to the traditional ANCOVA methods based on least squares fits. Our initial empirical results show that the validity of R procedures is similar to the least squares procedures. In terms of power, there is a small loss in efficiency to least squares methods when the random errors have a normal distribution but the rank-based procedures are much more powerful for the heavy-tailed error distributions in our study.

Rank-based analogs are also developed for pick-a-point, adjusted …

Survival Prediction For Brain Tumor Patients Using Gene Expression Data, Vinicius Bonato

Dissertations and Theses (Open Access)

Brain tumor is one of the most aggressive types of cancer in humans, with an estimated median survival time of 12 months and only 4% of the patients surviving more than 5 years after disease diagnosis. Until recently, brain tumor prognosis has been based only on clinical information such as tumor grade and patient age, but there are reports indicating that molecular profiling of gliomas can reveal subgroups of patients with distinct survival rates. We hypothesize that coupling molecular profiling of brain tumors with clinical information might improve predictions of patient survival time and, consequently, better guide future treatment decisions. …

General Coupon Collecting Models And Multinomial Games, James Y. Lee

UNLV Theses, Dissertations, Professional Papers, and Capstones

The coupon collection problem is one of the most studied problems in statistics. It is the problem of collecting r (r<∞) distinct coupons one by one from k different kinds (k<∞) of coupons. We note that this is equivalent to the classical occupancy problem which involves the random allocation of r distinct balls into k distinct cells. Although the problem was first introduced centuries ago, it is still actively investigated today. Perhaps its greatest feature is its versatility, numerous approaches, and countless variations. For this reason, we are particularly interested in creating a classification system for the many generalizations of the coupon collection problem. In this thesis, we will introduce models that will be able to categorize these generalizations. In addition, we calculate the waiting time for the models under consideration. Our approach is to use the Dirichlet Type II integral. We compare our calculations to the ones obtained through Monte Carlo simulation. Our results will show that our models and the method used to find the waiting times are ideal for solving problems of this type.

Goodness-Of-Fit And Change-Point Tests For Functional Data, Robertas Gabrys

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A test for independence and identical distribution of functional observations is proposed in this thesis. To reduce dimension, curves are projected on the most important functional principal components. Then a test statistic based on lagged cross--covariances of the resulting vectors is constructed. We show that this dimension reduction step introduces asymptotically negligible terms, i.e. the projections behave asymptotically as iid vector--valued observations. A complete asymptotic theory based on correlations of random matrices, functional principal component expansions, and Hilbert space techniques is developed. The test statistic has X²-square asymptotic null distribution.

Two inferential tests for error correlation in the …

Factors Affecting Reading Outcomes Across Time In Bureau Of Indian Education Reading First Schools, Heather J. Chapman

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Regardless of age, background, or socioeconomic status, children must learn to read in order to be successful in school and in their future careers. Reading is an essential skill necessary to be successful in all other academic content areas. Despite the importance of this skill, American Indian children consistently score below the national average on tests of reading ability and reading comprehension. During recent years, many schools in the Bureau of Indian Education (BIE) system requested funding through the Reading First initiative. Schools used the funding and support provided by the BIE Reading First grant to attempt system-wide change at …

Three Essays On Environmental- And Spatial-Based Valuation Of Urban Land And Housing, Lu Liu

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

This dissertation attempts to provide a comprehensive examination on the non-market valuation of the effect of open space amenities and local public infrastructure on the value of urban land and housing with both spatial heterogeneity and project heterogeneity. The demand for raw land is a derived demand for housing built on it. Therefore, we need to examine the land market and the housing market together. On the one hand, we estimate the value of urban land in a market that does not satisfy the usual assumptions of a competitive market structure as well as incentive incompatibility issues for transaction participants, …

Pre-Service Middle School Teachers’ Knowledge Of Algebraic Thinking, Marta Magiera, John Moyer, Leigh A. Van Den Kieboom

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study we examined the relationship between 18 pre-service middle school teachers’ own ability to use algebraic thinking to solve problems and their ability to recognize and interpret the algebraic thinking of middle school students. We assessed the pre-service teachers’ own algebraic thinking by examining their solutions and explanations to multiple algebra-based tasks posed during a semester-long mathematics content course. We assessed their ability to recognize and interpret the algebraic thinking of students in two ways. The first was by analyzing the preservice teachers’ ability to interpret students’ written solutions to open-ended algebra-based tasks. The second was by analyzing …

Pre-Service Teachers’ Knowledge Of Algebraic Thinking And The Characteristics Of The Questions Posed For Students, Leigh A. Van Den Kieboom, Marta Magiera, John Moyer

Mathematics, Statistics and Computer Science Faculty Research and Publications

In this study, we explored the relationship between the strength of pre-service teachers’ algebraic thinking and the characteristics of the questions they posed during cognitive interviews that focused on probing the algebraic thinking of middle school students. We developed a performance rubric to evaluate the strength of pre-service teachers’ algebraic thinking across 130 algebra-based tasks. We used an existing coding scheme found in the literature to analyze the characteristics of the questions pre-service teachers posed during clinical interviews. We found that pre-service teachers with higher algebraic thinking abilities were able to pose probing questions that uncovered student thinking through the …

A Numerical Method For Estimating The Variance Of Age At Maximum Growth Rate In Growth Models, Semhar Ogbagaber

Theses and Dissertations

Most studies on maturation and body composition using the Fels Longitudinal data mention peak height velocity (PHV) as an important outcome measure. The PHV is often derived from growth models such as the triple logistic model fitted to the stature (height) data. The age at PHV is sometimes ordinalized to designate an individual as an early, average or late maturer. In theory, age at PHV is the age at which the rate of growth reaches the maximum. Theoretically, for a well behaved growth function, this could be obtained by setting the second derivative of the growth function to zero and …

Multiple Regression Analysis: Sfa Professors' Salaries, Latonya Edmeade

Undergraduate Research Conference

There is always a certain curiosity and controversy surrounding professor’s salaries and whether they are overpaid or not paid enough. We have decided to try and untangle this wonder by creating a regression model in which the average person could easily understand while solving this lingering question. It is the average student’s opinion that professors make way too much compared to their daily tasks.

On the other hand, many professors are always complaining that they are not paid enough with their advanced degree and work load, not to mention the option always hovers over their head of pursuing a different …

War By Government: Which Systems Are Most Likely To Engage In Conflict?, Courtney Lemon

Undergraduate Research Conference

No abstract provided.

Default Rate On Auto Loans, Jessica Jones

Undergraduate Research Conference

In completing this model, we want to view a portfolio of loans at a bank and be able to predict the default rate on an auto loan. We also want to be able to look at an individual loan and predict the default probability taking into consideration interest rate, term, number of days late, times late, original loan amount, collateral value, LTV and credit score. The data will assist in forecasting default rates in future years and in projecting income and loss for a bank. We predict at the end of the model, credit score will be the main indicator …

Nonparametric Regression With Missing Outcomes Using Weighted Kernel Estimating Equations, Lu Wang, Andrea Rotnitzky, Xihong Lin

Harvard University Biostatistics Working Paper Series

No abstract provided.

Nonparametric And Semiparametric Analysis Of Current Status Data Subject To Outcome Misclassification, Victor G. Sal Y Rosas, James P. Hughes

UW Biostatistics Working Paper Series

In this article, we present nonparametric and semiparametric methods to analyze current status data subject to outcome misclassification. Our methods use nonparametric maximum likelihood estimation (NPMLE) to estimate the distribution function of the failure time when sensitivity and specificity may vary among subgroups. A nonparametric test is proposed for the two sample hypothesis testing. In regression analysis, we apply the Cox proportional hazard model and likelihood ratio based confidence intervals for the regression coefficients are proposed. Our methods are motivated and demonstrated by data collected from an infectious disease study in Seattle, WA.

Parameter Estimation In Linear-Linear Segmented Regression, Erika Lyn Hernandez

Theses and Dissertations

Segmented regression is a type of nonlinear regression that allows differing functional forms to be fit over different ranges of the explanatory variable. This paper considers the simple segmented regression case of two linear segments that are constrained to meet, often called the linear-linear model. Parameter estimation in the case where the joinpoint between the regimes is unknown can be tricky. Using a simulation study, four estimators for the parameters of the linear-linear model are evaluated. The bias and mean squared error of the estimators are considered under differing parameter combinations and sample sizes. Parameters estimated in the model are …