Applied Statistics Commons^™

Modeling And Fitting Two-Way Tables Containing Outliers, David L. Farnsworth

Articles

A model is proposed for two-way tables of measurement data containing outliers. The two independent variables are categorical and error free. Neither missing values nor replication are present. The model consists of the sum of a customary additive part that can be fit using least squares and a part that is composed of outliers. Recommendations are made for methods for identifying cells containing outliers and for fitting the model. A graph of the observations is used to determine the outliers’ locations. For all cells containing an outlier, replacement values are determined simultaneously using a classical missing-data tool. The result is …

Biasing Estimator To Mitigate Multicollinearity In Linear Regression Model, Abdulrasheed Bello Badawaire, Issam Dawoud, Adewale Folaranmi Lukman, Victoria Laoye, Arowolo Olatunji

Al-Bahir

A new two-parameter estimator was developed to combat the threat of multicollinearity for the linear regression model. Some necessary and sufficient conditions for the dominance of the proposed estimator over ordinary least squares (OLS) estimator, ridge regression estimator, Liu estimator, KL estimator, and some two-parameter estimators are obtained in the matrix mean square error sense. Theory and simulation results show that, under some conditions, the proposed two-parameter estimator consistently dominates other estimators considered in this study. The real-life application result follows suit.

A Statistical Analysis Of The Change In Age Distribution Of Spawning Hatchery Salmon, Rachel Macaulay, Emily Barrett, Grace Penunuri, Eli E. Goldwyn

Spora: A Journal of Biomathematics

Declines in salmon sizes have been reported primarily as a result of younger maturation rates. This change in age distribution poses serious threats to salmon-dependent peoples and ecological systems. We perform a statistical analysis to examine the change in age structure of spawning Alaskan chum salmon Oncorhynchus keta and Chinook salmon O. tshawytscha using 30 years of hatchery data. To highlight the impacts of this change, we investigate the average number of fry/smolt that each age of spawning chum/Chinook salmon produce. Our findings demonstrate an increase in younger hatchery salmon populations returning to spawn, and fewer amounts of fry produced …

Beyond Statistical Significance: A Holistic View Of What Makes A Research Finding "Important", Jane E. Miller

Numeracy

Students often believe that statistical significance is the only determinant of whether a quantitative result is “important.” In this paper, I review traditional null hypothesis statistical testing to identify what questions inferential statistics can and cannot answer, including statistical significance, effect size and direction, causality, generalizability, and changeability of the independent variable. I illustrate these issues with examples from an empirical study of the association between how much time teenagers spent playing video games and time spent reading. I describe how study design and context determine each of those aspects of “importance,” and close by summarizing how to provide a …

Problems With Machine Learning, High-Dimensional Data And Forecasting Stock Returns, Erik Mekelburg

Electronic Theses and Dissertations

Using a multi-level ensemble design, we forecast international stock market returns with a novel high-dimensional data set of aggregated cross sectional firm-level predictors. The method includes considerations of model uncertainty, parameter instability, model density and non-linearities with machine learning, shrinkage and model averaging. We provide evidence that it is important to systematically focus on all four sources of forecast failure, shed light on the sparsity/density debate in the stock return forecasting dialogue and contribute interesting findings on the efficacy dimensionality reduction with principal components analysis and partial least squares. The robustness of the approach is demonstrated through applications in four …

Lie Rings And Hall Basis Elements With Two Generators, Emma Schmidt, James Turner

Summer Research

A Lie ring is a set L with three operations: addition, subtraction, and the Lie bracket. The first two follow the usual rules of addition and subtraction.

Lie rings are said to be free if there are no further relations beyond these. A subset S in L is said to generate Lie ring L if every element of L can be expressed as a sum or difference of iterated brackets on elements of S.

Tennessee Brewconomy: Navigating The Wholesale Beer Tax Landscape, Lauren E. Dansbury

Science University Research Symposium (SURS)

In 2013, Tennessee transitioned from a price-based wholesale tax model to a per barrelage assessment. This research delves into the repercussions of this tax reform, assessing its impact on the brewing and wholesale distribution sectors. Despite the shift, Tennessee maintains the nation's highest wholesale beer tax for 16 consecutive years. The study examines the opportunity costs associated with this elevated tax, exploring alternative uses for the funds. Utilizing data on annual revenue collected by wholesalers from 2019 to 2022, segmented by city and county, the research provides actionable insights advocating for a reduction in the wholesale tax. The argument posits …

Statistical Tolerance Regions For Flexible Modeling Paradigms, Yafan Guo

Theses and Dissertations--Statistics

Tolerance intervals in a regression setting allow the user to quantify, with a specified degree of confidence, bounds for a specified proportion of the sampled population when conditioned on a set of covariate values. While methods are available for tolerance intervals in fully-parametric regression settings, the construction of tolerance intervals for semiparametric regression models has been treated in a limited capacity. The first project fills this gap and develops likelihood-based approaches for the construction of pointwise one-sided and two-sided tolerance intervals for semiparametric regression models. A numerical approach is also presented for constructing simultaneous tolerance intervals. An appealing facet of …

Enforcement Penalties At The Itc, Andrea R. Hugill, John C. Jarosz, Katherine D. Cappaert

Northwestern Journal of International Law & Business

The U.S. International Trade Commission (“ITC” or “Commission”) has grown in importance as a venue for U.S. companies to pursue intellectual property (“IP”) violators and to block the sale or importation of goods from overseas that infringe U.S. IP rights. Once a violation of the Section 337 of the Tariff Act of 1930 is found, an order halting further infringement, including importation, is almost always entered. In theory, potentially sizeable penalties may be imposed on entities that do not comply with the terms of an import restriction. In practice, the terms of an import restriction are almost always honored, but …

Forecasting Remission Time Of A Treatment Method For Leukemia As An Application To Statistical Inference Approach, Ahmed Galal Atia, Mahmoud Mansour, Rashad Mohamed El-Sagheer, B. S. El-Desouky

Basic Science Engineering

In this paper, Weibull-Linear Exponential distribution (WLED) has been investigated whether being it is a well-fit distribution to a clinical real data. These data represent the duration of remission achieved by a certain drug used in the treatment of leukemia for a group of patients. The statistical inference approach is used to estimate the parameters of the WLED through the set of the fitted data. The estimated parameters are utilized to evaluate the survival and hazard functions and hence assessing the treatment method through forecasting the duration of remission times of patients. A two-sample prediction approach has been applied to …

Classification Of Adult Income Using Decision Tree, Roland Fiagbe

Data Science and Data Mining

Decision tree is a commonly used data mining methodology for performing classification tasks. It is a tree-based supervised machine learning algorithm that is used to classify or make predictions in a path of how previous questions are answered. Generally, the decision tree algorithm categorizes data into branch-like segments that develop into a tree that contains a root, nodes, and leaves. This project seeks to explore the decision tree methodology and apply it to the Adult Income dataset from the UCI Machine Learning Repository, to determine whether a person makes over 50K per year and determine the necessary factors that improve …

Graphs Without A 2c3-Minor And Bicircular Matroids Without A U3,6-Minor, Daniel Slilaty

Mathematics and Statistics Faculty Publications

In this note we characterize all graphs without a 2C3-minor. A consequence of this result is a characterization of the bicircular matroids with no U3,6-minor.

Local Or Import? A Compositional Analysis Of Aztec Ritual Ceramics In The Tuxtlas Frontier, Veracruz, Mexico, Matthew T. Meyer

Murray State Theses and Dissertations

At the time of Spanish Contact in the early 16th Century the western Tuxtlas region formed part of the Aztec imperial frontier in the southern Gulf lowlands. The most apparent material manifestation of this imperial connection was Aztec-style Texcoco-Molded Censers, recovered primarily from sites that served local centralizing functions. While rare, these symbols may provide valuable information on the dynamics of frontier politics and the relations between this region and the distant core to which they were sending tax payments. Initial consideration of this adopted imperial style implies political linkages, but the mechanisms of introduction, knowledge transmission, imperial versus local …

Statistical Intervals For Neural Network And Its Relationship With Generalized Linear Model, Sheng Yuan

Theses and Dissertations--Statistics

Neural networks have experienced widespread adoption and have become integral in cutting-edge domains like computer vision, natural language processing, and various contemporary fields. However, addressing the statistical aspects of neural networks has been a persistent challenge, with limited satisfactory results. In my research, I focused on exploring statistical intervals applied to neural networks, specifically confidence intervals and tolerance intervals. I employed variance estimation methods, such as direct estimation and resampling, to assess neural networks and their performance under outlier scenarios. Remarkably, when outliers were present, the resampling method with infinitesimal jackknife estimation yielded confidence intervals that closely aligned with nominal …

Probabilistic Methods For Inferring The Order Of Pathway Alterations During Carcinogenesis And Cancer Subtype Classification, Menghan Wang

Theses and Dissertations--Statistics

Carcinogenesis is a complex process involving somatic mutations in a number of key biological pathways. Studying cancer evolution is an important task which contributes to better understanding of cancer biology and facilitates identification of new therapeutic targets. We focus on two important questions in cancer evolution. The first question is to delineating the temporal order of pathway mutations during tumorigenesis. And the other question is to cluster patients into biologically meaningful cancer subtypes. We present new statistical methods to 1)leverage functional annotations of mutations to enhance estimation of the order of pathway mutations during carcinogenesis, 2) incorporate intra-tumoral heterogeneity information …

Tolerance Intervals For Various Regression Models, Xitong Zhou

Theses and Dissertations--Statistics

Among statistical intervals, confidence intervals and prediction intervals are well-known and commonly used. In many applications, the problem becomes finding an interval that covers at least a certain proportion $P$ of the population for a characteristic of interest with a specified confidence level $(1-\alpha)$. And such interval is named a $P$-content, $(1-\alpha)$-confidence Tolerance Interval (TI). The topic of the dissertation is the utility of tolerance intervals for various regression models. We begin with a discussion of tolerance intervals for linear and nonlinear regression models. We then propose a bootstrap method of constructing TIs for Tobit regression to deal with censored …

Novel Modelling And Inference Considerations Involving The Exponentially-Modified Gaussian Distribution, Yanxi Li

Theses and Dissertations--Statistics

The exponentially-modified Gaussian (EMG) distribution is well-suited for analyzing data with positive skewness due to its characteristic positive skew from the exponential component. Despite its popularity in various fields, the EMG distribution has only been analyzed for univariate data without any regression settings. To address this limitation, we developed a generalized EMG regression model with covariates by assigning parametric functional forms to some or all of the parameters in the EMG distribution that vary with values of the covariates. To further perform data-clustering on observation points, we propose a competing regression model where the error structure is assumed to be …

Methodologies And Computational Tools For Zero-Inflated Discrete Weibull Models, Peng Yeh

Theses and Dissertations--Statistics

Count data with excess zeros is common in many fields, such as ecology, healthcare, and insurance. Excess zeros data are often causing the inaccurate fit from the count models. While zero-inflated models have been developing for over two decades, one should also consider a more flexible model that can handle the excess zeros and further over- or under-dispersion. In this talk, we discuss zero-inflated discrete Weibull model and some novel computational contributions. The flexibility and competitiveness of the ZIDW model are illustrated by simulation studies and a real data analysis. We also investigate the performance of the proposed model through …

Potential Alzheimer's Disease Plasma Biomarkers, Taylor Estepp

Theses and Dissertations--Epidemiology and Biostatistics

In this series of studies, we examined the potential of a variety of blood-based plasma biomarkers for the identification of Alzheimer's disease (AD) progression and cognitive decline. With the end goal of studying these biomarkers via mixture modeling, we began with a literature review of the methodology. An examination of the biomarkers with demographics and other health factors found evidence of minimal risk of confounding along the causal pathway from biomarkers to cognitive performance. Further study examined the usefulness of linear combinations of biomarkers, achieved via partial least squares (PLS) analysis, as predictors of various cognitive assessment scores and clinical …

The Impact Of Subjective Risk Analysis On Real Estate Prices In The Nisqually Region Following The 2001 Nisqually Earthquake, Ryan Espedal

All Master's Theses

Earthquakes are an environmental hazard that pose great risks to communities almost every day. With earthquakes, the main cause of concern is physical destruction of property, however, there are also psychological effects that are researched and discussed much less. In 2001, the Nisqually area of western Washington experienced a substantial earthquake that produced minimal physical damage but caused a significant decrease in real estate prices. Studying single-family homes from 1986-2012, this research utilizes hedonic property models to measure the change in consumer’s subjective risk calculations with reference to real estate purchases after the Nisqually earthquake, measure the relationship between earthquake …