Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, 2024 Purdue University Fort Wayne

#### Model Selection Through Cross-Validation For Supervised Learning Tasks With Manifold Data, Derek Brown

*The Journal of Purdue Undergraduate Research*

No abstract provided.

Sensitivity Analysis Of Prior Distributions In Regression Model Estimation, 2024 Department of Mathematics, Tai Solarin University of Education Ijagun Ogun State Nigeria.

#### Sensitivity Analysis Of Prior Distributions In Regression Model Estimation, Ayoade I Adewole, Oluwatoyin K. Bodunwa

*Al-Bahir Journal for Engineering and Pure Sciences*

Bayesian inferences depend solely on specification and accuracy of likelihoods and prior distributions of the observed data. The research delved into Bayesian estimation method of regression models to reduce the impact of some of the problems, posed by convectional method of estimating regression models, such as handling complex models, availability of small sample sizes and inclusion of background information in the estimation procedure. Posterior distributions are based on prior distributions and the data accuracy, which is the fundamental principles of Bayesian statistics to produce accurate final model estimates. Sensitivity analysis is an essential part of mathematical model validation in obtaining …

Exploration And Statistical Modeling Of Profit, 2023 East Tennessee State University

#### Exploration And Statistical Modeling Of Profit, Caleb Gibson

*Undergraduate Honors Theses*

For any company involved in sales, maximization of profit is the driving force that guides all decision-making. Many factors can influence how profitable a company can be, including external factors like changes in inflation or consumer demand or internal factors like pricing and product cost. Understanding specific trends in one's own internal data, a company can readily identify problem areas or potential growth opportunities to help increase profitability.

In this discussion, we use an extensive data set to examine how a company might analyze their own data to identify potential changes the company might investigate to drive better performance. Based …

The Private Pilot Check Ride: Applying The Spacing Effect Theory To Predict Time To Proficiency For The Practical Test, 2023 Florida Institute of Technology - Melbourne

#### The Private Pilot Check Ride: Applying The Spacing Effect Theory To Predict Time To Proficiency For The Practical Test, Michael Scott Harwin

*Theses and Dissertations*

This study examined the relationship between a set of targeted factors and the total flight time students needed to become ready to take the private pilot check ride. The study was grounded in Ebbinghaus’s (1885/1913/2013) forgetting curve theory and spacing effect, and Ausubel’s (1963) theory of meaningful learning. The research factors included (a) training time to proficiency, which represented the number of training days needed to become check-ride ready; (b) flight training program (Part 61 vs. Part 141); (c) organization offering the training program (2- or 4-year college/university vs. FBO); (d) scheduling policy (mandated vs. student-driven); and demographical variables, which …

Nonparametric Derivative Estimation Using Penalized Splines: Theory And Application, 2023 University of Massachusetts Amherst

#### Nonparametric Derivative Estimation Using Penalized Splines: Theory And Application, Bright Antwi Boasiako

*Doctoral Dissertations*

This dissertation is in the field of Nonparametric Derivative Estimation using

Penalized Splines. It is conducted in two parts. In the first part, we study the L2

convergence rates of estimating derivatives of mean regression functions using penalized splines. In 1982, Stone provided the optimal rates of convergence for estimating derivatives of mean regression functions using nonparametric methods. Using these rates, Zhou et. al. in their 2000 paper showed that the MSE of derivative estimators based on regression splines approach zero at the optimal rate of convergence. Also, in 2019, Xiao showed that, under some general conditions, penalized spline estimators …

Statistical Inference On Lung Cancer Screening Using The National Lung Screening Trial Data., 2023 University of Louisville

#### Statistical Inference On Lung Cancer Screening Using The National Lung Screening Trial Data., Farhin Rahman

*Electronic Theses and Dissertations*

This dissertation consists of three research projects on cancer screening probability modeling. In these projects, the three key modeling parameters (sensitivity, sojourn time, transition density) for cancer screening were estimated, along with the long-term outcomes (including overdiagnosis as one outcome), the optimal screening time/age, the lead time distribution, and the probability of overdiagnosis at the future screening time were simulated to provide a statistical perspective on the effectiveness of cancer screening programs. In the first part of this dissertation, a statistical inference was conducted for male and female smokers using the National Lung Screening Trial (NLST) chest X-ray data. A …

A Comparison Of Confidence Intervals In State Space Models, 2023 Southern Methodist University

#### A Comparison Of Confidence Intervals In State Space Models, Jinyu Du

*Statistical Science Theses and Dissertations*

This thesis develops general procedures for constructing confidence intervals (CIs) of the error disturbance parameters (standard deviations) and transformations of the error disturbance parameters in time-invariant state space models (ssm). With only a set of observations, estimating individual error disturbance parameters accurately in the presence of other unknown parameters in ssm is a very challenging problem. We attempted to construct four different types of confidence intervals, Wald, likelihood ratio, score, and higher-order asymptotic intervals for both the simple local level model and the general time-invariant state space models (ssm). We show that for a simple local level model, both the …

Addressing The Impact Of Time-Dependent Social Groupings On Animal Survival And Recapture Rates In Mark-Recapture Studies, 2023 The University of Western Ontario

#### Addressing The Impact Of Time-Dependent Social Groupings On Animal Survival And Recapture Rates In Mark-Recapture Studies, Alexandru M. Draghici

*Electronic Thesis and Dissertation Repository*

Mark-recapture (MR) models typically assume that individuals under study have independent survival and recapture outcomes. One such model of interest is known as the Cormack-Jolly-Seber (CJS) model. In this dissertation, we conduct three major research projects focused on studying the impact of violating the independence assumption in MR models along with presenting extensions which relax the independence assumption. In the first project, we conduct a simulation study to address the impact of failing to account for pair-bonded animals having correlated recapture and survival fates on the CJS model. We examined the impact of correlation on the likelihood ratio test (LRT), …

Testing For Dice Control Based On Observations Of The Length Of The Shooter's Hand, 2023 University of Utah

#### Testing For Dice Control Based On Observations Of The Length Of The Shooter's Hand, Stewart N. Ethier, Hokwon Cho

*International Conference on Gambling & Risk Taking*

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Uconn Baseball Batting Order Optimization, 2023 University of Connecticut

#### Uconn Baseball Batting Order Optimization, Gavin Rublewski, Gavin Rublewski

*Honors Scholar Theses*

Challenging conventional wisdom is at the very core of baseball analytics. Using data and statistical analysis, the sets of rules by which coaches make decisions can be justified, or possibly refuted. One of those sets of rules relates to the construction of a batting order. Through data collection, data adjustment, the construction of a baseball simulator, and the use of a Monte Carlo Simulation, I have assessed thousands of possible batting orders to determine the roster-specific strategies that lead to optimal run production for the 2023 UConn baseball team. This paper details a repeatable process in which basic player statistics …

Two Sample Statistical Test For Location Parameters, 2023 Panjab University, Chandigarh

#### Two Sample Statistical Test For Location Parameters, Narinder Kumar, Arun Kumar

*Journal of Modern Applied Statistical Methods*

A class of distribution-free tests for the homogeneity of location parameters is proposed and compared with different competitors in terms of Pitman asymptotic relative efficiency. A numerical example is provided and a simulation study is made to check the performance of the tests.

High-Dimensional Variable Selection Via Knockoffs Using Gradient Boosting, 2023 Western Michigan University

#### High-Dimensional Variable Selection Via Knockoffs Using Gradient Boosting, Amr Essam Mohamed

*Dissertations*

As data continue to grow rapidly in size and complexity, efficient and effective statistical methods are needed to detect the important variables/features. Variable selection is one of the most crucial problems in statistical applications. This problem arises when one wants to model the relationship between the response and the predictors. The goal is to reduce the number of variables to a minimal set of explanatory variables that are truly associated with the response of interest to improve the model accuracy. Effectively choosing the true influential variables and controlling the False Discovery Rate (FDR) without sacrificing power has been a challenge …

High Dimensional Data Analysis: Variable Screening And Inference, 2023 University of Kentucky

#### High Dimensional Data Analysis: Variable Screening And Inference, Lei Fang

*Theses and Dissertations--Statistics*

This dissertation focuses on the problem of high dimensional data analysis, which arises in many fields including genomics, finance, and social sciences. In such settings, the number of features or variables is much larger than the number of observations, posing significant challenges to traditional statistical methods.

To address these challenges, this dissertation proposes novel methods for variable screening and inference. The first part of the dissertation focuses on variable screening, which aims to identify a subset of important variables that are strongly associated with the response variable. Specifically, we propose a robust nonparametric screening method to effectively select the predictors …

Bayesian Methods For Graphical Models With Neighborhood Selection., 2022 University of Louisville

#### Bayesian Methods For Graphical Models With Neighborhood Selection., Sagnik Bhadury

*Electronic Theses and Dissertations*

Graphical models determine associations between variables through the notion of conditional independence. Gaussian graphical models are a widely used class of such models, where the relationships are formalized by non-null entries of the precision matrix. However, in high-dimensional cases, covariance estimates are typically unstable. Moreover, it is natural to expect only a few significant associations to be present in many realistic applications. This necessitates the injection of sparsity techniques into the estimation method. Classical frequentist methods, like GLASSO, use penalization techniques for this purpose. Fully Bayesian methods, on the contrary, are slow because they require iteratively sampling over a quadratic …

Mle And Eap Methods For Estimating Ability Scores For Data Of Varying Sample Size And Item Length, 2022 University of Arkansas, Fayetteville

#### Mle And Eap Methods For Estimating Ability Scores For Data Of Varying Sample Size And Item Length, Sahar Taji

*Graduate Theses and Dissertations*

In this research, the performance of two popular estimators, Maximum Likelihood Estimator(MLE) and Bayesian Expected a Posteriori (EAP) is studied and compared in estimating the latent ability score in an Item Response Theory (IRT) model. The 2-Parameter Logistic (2PL) IRT model which is characterized by difficulty and discrimination item parameters is used to estimate the latent ability scores. Several datasets are generated for variety of sample size and item length values. The Monte-Carlo simulation is used to analyze the performance of the estimators. Results show that MLE produces reliable results with low root mean square error (RMSE) across all datasets. …

Functional Data Analysis Of Covid-19, 2022 University of New Mexico

#### Functional Data Analysis Of Covid-19, Nichole L. Fluke

*Mathematics & Statistics ETDs*

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1^{st}, 2020 and goes through March 31^{st}, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …

Statistical Roles Of The G-Expectation Framework In Model Uncertainty: The Semi-G-Structure As A Stepping Stone, 2022 The University of Western Ontario

#### Statistical Roles Of The G-Expectation Framework In Model Uncertainty: The Semi-G-Structure As A Stepping Stone, Yifan Li

*Electronic Thesis and Dissertation Repository*

The G-expectation framework is a generalization of the classical probability system based on the sublinear expectation to deal with phenomena that cannot be described by a single probabilistic model. These phenomena are closely related to the long-existing concern about model uncertainty in statistics. However, the distributions and independence in the G-framework are quite different from the classical setup. These distinctions bring difficulty when applying the idea of this framework to general statistical practice. Therefore, a fundamental and unavoidable problem is how to better understand G-version concepts from a statistical perspective.

To explore this problem, this thesis establishes a new substructure …

Bayesian Estimation Of The Intensity Function Of A Non-Homogeneous Poisson Process, 2022 Jacksonville State University

#### Bayesian Estimation Of The Intensity Function Of A Non-Homogeneous Poisson Process, James Jensen

*Theses*

In this paper we explore Bayesian inference and its application to the problem of estimating the intensity function of a non-homogeneous Poisson process. These processes model the behavior of phenomena in which one or more events, known as arrivals, occur independently of one another over a certain period of time. We are concerned with the number of events occurring during particular time intervals across several realizations of the process. We show that given sufficient data, we are able to construct a piecewise-constant function which accurately estimates the mean rates on particular intervals. Further, we show that as we reduce these …

The Q-Analogue Of The Extended Generalized Gamma Distribution, 2022 Western University

#### The Q-Analogue Of The Extended Generalized Gamma Distribution, Wenhao Chen

*Undergraduate Student Research Internships Conference*

This project introduces a flexible univariate probability model referred to as the q-analogue of the Extended Generalized Gamma (or q-EGG) distribution, which encompasses the majority of the most frequently used continuous distributions, including the gamma, Weibull, logistic, type-1 and type-2 beta, Gaussian, Cauchy, Student-t and F. Closed form representations of its moments and cumulative distribution function are provided. Additionally, computational techniques are proposed for determining estimates of its parameters. Both the method of moments and the maximum likelihood approach are utilized. The effect of each parameter is also graphically illustrated. Certain data sets are modeled with q-EGG distributions; goodness of …

To Logit Or Not To Logit Data In The Unit Interval: A Simulation Study, 2022 University of Windsor

#### To Logit Or Not To Logit Data In The Unit Interval: A Simulation Study, Kayode Idris Hamzat

*Major Papers*

In this paper, we recommend a mechanism for determining whether to logit or not to logit data in the unit interval which is based on quantile estimation of data between 0 and 1. By using a simulated dataset generated from a Beta regression model, the estimated quantile for this model perform better than those based on the linear quantile regression with logit transformation.

Further, we investigate the performance of the quantile regression estimators based on the LQR and we conclude that it is better than those based on the Beta regression when the distribution is contaminated with 10% uniform numbers …