Applied Statistics Commons^™

Bayesian Inference On The Variance Of Normal Distribution Using Moving Extremes Ranked Set Sampling, Said Ali Al-Hadhrami, Amer Ibrahim Al-Omari

Journal of Modern Applied Statistical Methods

Bayesian inference of the variance of the normal distribution is considered using moving extremes ranked set sampling (MERSS) and is compared with the simple random sampling (SRS) method. Generalized maximum likelihood estimators (GMLE), confidence intervals (CI), and different testing hypotheses are considered using simple hypothesis versus simple hypothesis, simple hypothesis versus composite alternative, and composite hypothesis versus composite alternative based on MERSS and compared with SRS. It is shown that modified inferences using MERSS are more efficient than their counterparts based on SRS.

Quantifying Bimodality Part 2: A Likelihood Ratio Test For The Comparison Of A Unimodal Normal Distribution And A Bimodal Mixture Of Two Normal Distributions. Bruno D. Zumbo Is, B. W. Frankland, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

Scientists in a variety of fields are often faced with the question of whether a sample is best described as unimodal or bimodal. In an earlier paper (Frankland & Zumbo, 2002), a simple and convenient method for assessing bimodality was described. That method is extended by developing and demonstrating a likelihood ratio test (LRT) for bimodality for the comparison of a unimodal normal distribution and a bimodal mixture of two normal distributions. As in Frankland and Zumbo (2002), the LRT approach is demonstrated using algorithms in SPSS.

Email: A Note On Hypothesis Tests After Correction For Autocorrelation: Solace For The Cochrane-Orcutt Method?, Terry E. Dielman

Journal of Modern Applied Statistical Methods

The behavior of the t test in small samples for coefficient significance in time-series regressions is examined after using the Prais-Winsten (PW) and Cochrane-Orcutt (CO) corrections for autocorrelation. Results are compared to ordinary least squares and generalized least squares.

Quel Test For Two Linear Restrictions In The Nonlinear Models, Krishna K. Saha

Journal of Modern Applied Statistical Methods

An alternative Wald type test called the quel test is developed for two linear restrictions by finding the critical region based on the quel utilizing the repeated values of estimated parameters of interest under the null. Simulation shows evidence that the full quel test performs best in that it holds nominal level well and shows monotonic increasing power properties.

Comparative Power Of The Independent T, Permutation T, And Wilcoxontests, Michèle Weber, Shlomo Sawilowsky

Journal of Modern Applied Statistical Methods

The nonparametric Wilcoxon Rank Sum (also known as the Mann-Whitney U) and the permutation t-tests are robust with respect to Type I error for departures from population normality, and both are powerful alternatives to the independent samples Student’s t-test for detecting shift in location. The question remains regarding their comparative statistical power for small samples, particularly for non-normal distributions. Monte Carlo simulations indicated the rank-based Wilcoxon test was found to be more powerful than both the t and the permutation t-tests.

Industrialization In Animal Agriculture: A Kalman Filter Analysis, Oya S. Erdogdu, Levent Ozbek

Journal of Modern Applied Statistical Methods

Studies discussing the effects of technological developments on (animal) agricultural production argue that the effective usage of chemicals and genetic engineering increase control over production processes, which in turn decreases seasonality (one significant factor defining agricultural production) significantly and brings standardization to production. Studies on broilery also show that production is not limited by nature determined seasons. Supply side changes accompanied by changes in demand have led to more healthier, standardized products. Using tools of economics and statistics, this study documents this transformation in animal agricultural production of beef, pork and milk. Results indicate decreasing seasonality, thus the industralization of …

Aligned Rank Tests For Interactions In Split-Plot Designs: Distributional Assumptions And Stochastic Heterogeneity, T. Mark Beasley, Bruno D. Zumbo

Journal of Modern Applied Statistical Methods

Three aligned rank methods for transforming data from multiple group repeated measures (split-plot) designs are reviewed. Univariate and multivariate statistics for testing the interaction in split-plot designs are elaborated. Computational examples are presented to provide a context for performing these ranking procedures and statistical tests. SAS/IML and SPSS syntax code to perform the procedures is included in the Appendix.

Pain As A Predictor Of Depression Treatment Outcomes In Women With Childhood Sexual Abuse, Ellen L. Poleshuck, Nancy L. Talbot, Haiyan Su, Xin Tu, Linda Chaudron, Stephanie Gamble, Donna E. Giles

Department of Applied Mathematics and Statistics Faculty Scholarship and Creative Works

Objectives: Childhood sexual abuse (CSA) increases risk for both depression and pain in women. Pain is associated with worse depression treatment response. The contribution of pain to depression treatment outcomes in women with histories of CSA is unknown. This study examined whether clinically significant pain would be associated with worse depression and functioning outcomes among women with CSA histories treated with interpersonal psychotherapy. Method: Participants were 66 women with major depression and CSA who presented to a community mental health center. An interpersonal psychotherapy protocol planned for 14 weekly sessions followed by 2 biweekly sessions. Patients were classified as experiencing …

The Comparison Of Model Selection Criteria When Selecting Among Competing Hierarchical Linear Models, Tiffany A. Whittaker, Carolyn F. Furlow

Journal of Modern Applied Statistical Methods

Little is known about the use and accuracy of model selection criteria when selecting among a set of competing multilevel models. The practices of applied researchers and the performance of five model selection criteria are examined when selecting the correct multilevel model using simulation techniques.

Bias In Stabilized Sieve Sampling, Liming Guan, John P. Wendell

Journal of Modern Applied Statistical Methods

The stabilized sieve sample selection method (SSM) is considered to be a probability proportional to size (PPS) sampling method with an unbiased estimator (Horgan 1997, 1998). This article demonstrates that SSM does not select items with PPS and that the point estimator is biased.

A New Approximate Bayesian Approach For Decision Making About The Variance Of A Gaussian Distribution Versus The Classical Approach, Vincent A. R. Camara

Journal of Modern Applied Statistical Methods

Rules of decision-making about the variance of a Gaussian distribution are obtained and compared. Considering the square error loss function, an approximate Bayesian decision rule for the variance of a normal population is derived. Using normal data and SAS software, the obtained approximate Bayesian test results were compared to their counterparts obtained with the well-known classical decision rule. It is shown that the proposed approximate Bayesian decision rule relies only on observations. The classical decision rule, which uses the Chi-square statistic, does not always yield the best results: the proposed approach often performs better.

Which Is The Best Parametric Statistical Method For Analyzing Delphi Data?, Hiral A. Shah, Sema A. Kalaian

Journal of Modern Applied Statistical Methods

This study compares the three parametric statistical methods: coefficient of variation, Pearson correlation coefficient, and F-test to obtain reliability in a Delphi study that involved more than 100 participants. The results of this study indicated that coefficient of variation was the best procedure to obtain reliability in such a study.

A Socratic Dialogue, Vance W. Berger

Journal of Modern Applied Statistical Methods

Socrates has found some aspects of medical biostatistics a bit confusing, and wishes to discuss some of these issues with Simplicio, a prominent medical researcher. This Socratic dialogue will shed some light on the errant use of parametric analyses in clinical trials.

A Comparison Of Maximum Likelihood And Expected A Posteriori Estimation For Polychoric Correlation Using Monte Carlo Simulation, Jinsong Chen, Jaehwa Choi

Journal of Modern Applied Statistical Methods

This study aims to compare the maximum likelihood (ML) and expected a posterior (EAP) estimation for polychoric correlation (PCC) under diverse conditions, especially when considering a sample size. As the ML is the classical solution to estimate PCC, the EAP is a new method based on Bayes’ theorem. Different types of prior distributions are also adapted to investigate the sensitivity of prior distribution onto the PCC estimate for the EAP case. The Monte Carlo simulation is used for this comparison by a specialized program code in MATLAB.

Detecting Near-Earth Objects Using Cross-Correlation With A Point Spread Function, Anthony P. O'Dell

Theses and Dissertations

This thesis describes a process to help discover Near-Earth Objects (NEOs) of larger than 140 meters in diameter from ground based telescopes. The process involves using Nyquist sampling rate to take data from a ground-based telescope and measuring the atmospheric seeing parameter, r₀, at the time of data collection. r0 is then used to create a point spread function (PSF) for a NEO at the visual magnitude limit of the telescope and exposure time. This PSF is cross-correlated with the Nyquist sampling rate image from the telescope to reduce the noise and therefore increase the detection probability of …

A Berry-Esseen Theorem For Sample Quantiles Under Weak Dependence, S. N. Lahiri, Shuxia Sun

Mathematics and Statistics Faculty Publications

This paper proves a Berry-Esseen theorem for sample quantiles of strongly-mixing random variables under a polynomial mixing rate. The rate of normal approximation is shown to be O(n^-1/2) as n -> infinity, where n denotes the sample size. This result is in sharp contrast to the case of the sample mean of strongly-mixing random variables where the rate O(n^-1/2) is not known even under an exponential strong mixing rate. The main result of the paper has applications in finance and econometrics as financial time series important data often are heavy-tailed and quantile …

Comments On "Getting Scarred And Winning Lotteries: Effects Of Exemplar Cuing And Statistical Format On Imagining Low-Probability Events," By Newell, Mitchell, And Hayes (2008), Jonathan Koehler, Laura Macchi

Faculty Working Papers

Newell, Mitchell, and Hayes (NMH) conduct three experiments designed to test whether exemplar cuing (EC) theory or a statistical format theory provides a more accurate account for how people make judgments about low-probability events. They report finding support for the statistical format theory and little or no support for EC. However, NMH misstate the requirements for the production of exemplars in EC theory. As a result, they confuse non-exemplar conditions with exemplar conditions in their experiments, and find results that are virtually irrelevant to EC theory.

Why Study Applied/Agricultural Economics, Matt Bogard

Agriculture Department Seminar Series

Agricultural Economics is a very applied field covering many topics beyond those stereotypically thought of as pertaining to agriculture. These may include finance and risk management, environmental and natural resource economics, game theory, or public policy analysis to name a few.

A Direct Solution Of The Robin Inverse Problem, Weifu Fang, Suxing Zeng

Mathematics and Statistics Faculty Publications

We present a direct, linear boundary integral equation method for the inverse problem of recovering the Robin coefficient from a single partial boundary measurement of the solution to the Laplace equation.

The Deterrent Effect Of Death Penalty Eligibility: Evidence From The Adoption Of Child Murder Eligibility Factors, Michael D. Frakes, Matthew Harding

Faculty Scholarship

We draw on within-state variations in the reach of capital punishment statutes between 1977 and 2004 to identify the deterrent effects associated with capital eligibility. Focusing on the most prevalent eligibility expansion, we estimate that the adoption of a child murder factor is associated with an approximately 20% reduction in the homicide rate of youth victims. Eligibility expansions may enhance deterrence by (1) paving the way for more executions and (2) providing prosecutors with greater leverage to secure enhanced non-capital sentences. While executions themselves are rare, this latter channel is likely to be triggered fairly regularly, providing a reasonable basis …

A Note On The Positive Solutions Of An Inhomogeneous Elliptic Equation On Rn, Yinbin Deng, Yi Li, Fen Yang

Mathematics and Statistics Faculty Publications

This paper is contributed to the elliptic equation

(0.1) Δu+K(|x|)up+μf(|x|)=0,

where p>1, x∈Rn, n⩾3, and μ⩾0 is a constant. We study the structure of positive radial solutions of (0.1) and obtain the uniqueness of solution decaying faster than r−m at ∞ if μ is small enough under some assumptions on K and f, where m is the slow decay rate.

Periodic Traveling Waves In Sirs Endemic Models, Tong Li, Yi Li, Herbert W. Hethcote

Mathematics and Statistics Faculty Publications

Mathematical models are used to determine if infection wave fronts could occur by traveling geographically in a loop around a region or continent. These infection wave fronts arise by Hopf bifurcation for some spatial models for infectious disease transmission with distributed-contacts. Periodic traveling waves are shown to exist for the spatial analog of the SIRS endemic model, in which the temporary immunity is described by a delay, but they do not exist in a similar spatial SIRS endemic model without a delay. Specifically, we found that the ratio of the delay ω in the recovered class and the average infectious …

Extending The Skill Test For Disease Diagnosis, Shu-Chuan Lin, Paul H. Kvam, Jye-Chyi Lu

Department of Math & Statistics Faculty Publications

For diagnostic tests, we present an extension to the skill plot introduced by Briggs and Zaretski (Biometrics 2008; 64:250–261). The method is motivated by diagnostic measures for osteopetrosis in a study summarized by Hans et al. (The Lancet 1996; 348:511–514). Diagnostic test accuracy is typically defined using the area (or partial area) under the receiver operator characteristic (ROC) curve. If partial area is used, the resulting statistic can be highly subjective because the focus region of the ROC curve corresponds to a set of low false‐positive rates that are chosen by the experimenter. This paper introduces a more …

Probe-Level Statistical Models For Differential Expression Of Genes In Bovine Nt Studies, Jason L. Bell

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

A brief introduction of microarray technology and its uses is given. This technology is commonly used in agricultural research, including research in nuclear transfer, which motivated this study. There are 3 classes of statistical models compared: probeset-level, weighted probeset-level and probe-level.

Different statistical mod els are compared on 3 spike-in experiments to assess the relative performance in identifying differentially expressed genes . A novel nested factorial model was found to outperform all other models compared in this study in one spike-in experiment, and was found to be competitive in its performance relative to the other models on the other spike-in …

Comparison Of Random Forests And Cforest: Variable Importance Measures And Prediction Accuracies, Rong Xia

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

Random forests are ensembles of trees that give accurate predictions for regression, classification and clustering problems. The CART tree, the base learn er employed by random forests, has been criticized because of bias in the selection of splitting variables. The performance of random forests is suspect due to this criticism. A new implementation of random forests, Cforest, which is claimed to outperform random forests in both predictive power and variable importance measures , was developed based on Ctree, an implementation of conditional inference trees.

We address the underlying mechanism of random forests and Cforest in this report. Comparison of random …

Statistical Methods In Microarray Data Analysis, Liping Huang

University of Kentucky Doctoral Dissertations

This dissertation includes three topics. First topic: Regularized estimation in the AFT model with high dimensional covariates. Second topic: A novel application of quantile regression for identification of biomarkers exemplified by equine cartilage microarray data. Third topic: Normalization and analysis of cDNA microarray using linear contrasts.

Statistical Inferences For Functions Of Parameters Of Several Pareto And Exponential Populations With Application In Data Traffic, Sumith Gunasekera

UNLV Theses, Dissertations, Professional Papers, and Capstones

In this dissertation, we discuss the usability and applicability of three statistical inferential frameworks--namely, the Classical Method, which is sometimes referred to as the Conventional or the Frequentist Method, based on the approximate large sample approach, the Generalized Variable Method based on the exact generalized p -value approach, and the Bayesian Method based on prior densities--for solving existing problems in the area of parametric estimation. These inference procedures are discussed through Pareto and exponential distributions that are widely used to model positive random variables relevant to social, scientific, actuarial, insurance, finance, investments, banking, and many other types of observable phenomena. …