Applied Statistics Commons^™

Parametric, Nonparametric, And Semiparametric Linear Regression In Classical And Bayesian Statistical Quality Control, Chelsea L. Jones

Theses and Dissertations

Statistical process control (SPC) is used in many fields to understand and monitor desired processes, such as manufacturing, public health, and network traffic. SPC is categorized into two phases; in Phase I historical data is used to inform parameter estimates for a statistical model and Phase II implements this statistical model to monitor a live ongoing process. Within both phases, profile monitoring is a method to understand the functional relationship between response and explanatory variables by estimating and tracking its parameters. In profile monitoring, control charts are often used as graphical tools to visually observe process behaviors. We construct a …

Nonparametric Tests Of Lack Of Fit For Multivariate Data, Yan Xu

Theses and Dissertations--Statistics

A common problem in regression analysis (linear or nonlinear) is assessing the lack-of-fit. Existing methods make parametric or semi-parametric assumptions to model the conditional mean or covariance matrices. In this dissertation, we propose fully nonparametric methods that make only additive error assumptions. Our nonparametric approach relies on ideas from nonparametric smoothing to reduce the test of association (lack-of-fit) problem into a nonparametric multivariate analysis of variance. A major problem that arises in this approach is that the key assumptions of independence and constant covariance matrix among the groups will be violated. As a result, the standard asymptotic theory is not …

Evaluation Of Using The Bootstrap Procedure To Estimate The Population Variance, Nghia Trong Nguyen

Electronic Theses and Dissertations

The bootstrap procedure is widely used in nonparametric statistics to generate an empirical sampling distribution from a given sample data set for a statistic of interest. Generally, the results are good for location parameters such as population mean, median, and even for estimating a population correlation. However, the results for a population variance, which is a spread parameter, are not as good due to the resampling nature of the bootstrap method. Bootstrap samples are constructed using sampling with replacement; consequently, groups of observations with zero variance manifest in these samples. As a result, a bootstrap variance estimator will carry a …

Power And Sample Size Estimation For Nonparametric Composite Endpoints: Practical Implementation Using Data Simulations, Paul M. Brown, Justin A. Ezekowitz

Journal of Modern Applied Statistical Methods

Composite endpoints are a popular outcome in controlled studies. However, the required sample size is not easily obtained due to the assortment of outcomes, correlations between them and the way in which the composite is constructed. Data simulations are required. A macro is developed that enables sample size and power estimation.

Examination And Comparison Of The Performance Of Common Non-Parametric And Robust Regression Models, Gregory F. Malek

Electronic Theses and Dissertations

ABSTRACT

Examination and Comparison of the Performance of Common Non-Parametric and Robust Regression Models

By

Gregory Frank Malek

Stephen F. Austin State University, Masters in Statistics Program,

Nacogdoches, Texas, U.S.A.

g_m_2002@live.com

This work investigated common alternatives to the least-squares regression method in the presence of non-normally distributed errors. An initial literature review identified a variety of alternative methods, including Theil Regression, Wilcoxon Regression, Iteratively Re-Weighted Least Squares, Bounded-Influence Regression, and Bootstrapping methods. These methods were evaluated using a simple simulated example data set, as well as various real data sets, including math proficiency data, Belgian telephone call data, and faculty …

Outlier Impact And Accommodation On Power, Hongjing Liao, Yanju Li, Gordon P. Brooks

Journal of Modern Applied Statistical Methods

The outliers’ influence on power rates in ANOVA and Welch tests at various conditions was examined and compared with the effectiveness of nonparametric methods and Winsorizing in minimizing the impact of outliers. Results showed that, considering both power and Type I error, a nonparametric test is the safest choice to control the inflation of Type I error with a decent sample size and yield relatively high power.

Comparison Of Some Multivariate Nonparametric Tests In Profile Analysis To Repeated Measurements, Mehrdad Vossoughi, Shila Shahvali, Erfan Sadeghi

Journal of Modern Applied Statistical Methods

Through Monte Carlo simulations, the performance of six multivariate nonparametric tests for testing the hypothesis of parallelism in profile analysis was studied. In conclusion, the tests based on ranks were as efficient as Hotelling's T² under multivariate normal distribution. For the heavy tailed distribution, the tests based on signs performed best.

A Monte Carlo Comparison Of Robust Manova Test Statistics, Holmes Finch, Brian French

Journal of Modern Applied Statistical Methods

Multivariate Analysis of Variance (MANOVA) is a popular statistical tool in the social sciences, allowing for the comparison of mean vectors across groups. MANOVA rests on three primary assumptions regarding the population: (a) multivariate normality, (b) equality of group population covariance matrices and (c) independence of errors. When these assumptions are violated, MANOVA does not perform well with respect to Type I error and power. There are several alternative test statistics that can be considered including robust statistics and the use of the structural equation modeling (SEM) framework. This simulation study focused on comparing the performance of the P test …

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 …

Length Bias In The Measurements Of Carbon Nanotubes, Paul H. Kvam

Department of Math & Statistics Faculty Publications

To measure carbon nanotube lengths, atomic force microscopy and special software are used to identify and measure nanotubes on a square grid. Current practice does not include nanotubes that cross the grid, and, as a result, the sample is length-biased. The selection bias model can be demonstrated through Buffon’s needle problem, extended to general curves that more realistically represent the shape of nanotubes observed on a grid. In this article, the nonparametric maximum likelihood estimator is constructed for the length distribution of the nanotubes, and the consequences of the length bias are examined. Probability plots reveal that the corrected length …

Comparison Of The T Vs. Wilcoxon Signed-Rank Test For Likert Scale Data And Small Samples, Gary E. Meek, Ceyhun Ozgur, Kenneth Dunning

Journal of Modern Applied Statistical Methods

The one sample t-test is compared with the Wilcoxon Signed-Rank test for identical data sets representing various Likert scales. An empirical approach is used with simulated data. Comparisons are based on observed error rates for 27,850 data sets. Recommendations are provided.

Jmasm 26: Hettmansperger And Mckean Linear Model Aligned Rank Test For The Single Covariate And One-Way Ancova Case (Sas), Paul A. Nakonezny, Robert D. Shull

Journal of Modern Applied Statistical Methods

A SAS program (SAS 9.1.3 release, SAS Institute, Cary, N.C.) is presented to implement the Hettmansperger and McKean (1983) linear model aligned rank test (nonparametric ANCOVA) for the single covariate and one-way ANCOVA case. As part of this program, SAS code is also provided to derive the residuals from the regression of Y on X (which is step 1 in the Hettmansperger and McKean procedure) using either ordinary least squares regression (proc reg in SAS) or robust regression with MM estimation (proc robustreg in SAS).

A Conversation With R. Clifford Blair On The Occasion Of His Retirement, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

An interview was conducted on 23 November 2003 with R. Clifford Blair on the occasion on his retirement from the University of South Florida. This article is based on that interview. Biographical sketches and images of members of his academic genealogy are provided.

A Nonparametric Fitted Test For The Behrens-Fisher Problem, Terry Hyslop, Paul J. Lupinacci

Journal of Modern Applied Statistical Methods

A nonparametric test for the Behrens-Fisher problem that is an extension of a test proposed by Fligner and Policello was developed. Empirical level and power estimates of this test are compared to those of alternative nonparametric and parametric tests through simulations. The results of our test were better than or comparable to all tests considered.

Variance Testing With Simplicial Data Depth, Karen J. Mcgaughey, George A. Milliken

Conference on Applied Statistics in Agriculture

A method is developed and studied for testing equality of variances based on simplicial data depth and Mood's nonparametric test in the case of two samples. A method for calculating univariate simplicial data depth using a rank transformation is introduced. Type I error rates and power curves are compared for three existing tests for equality of variances and the data depth test using data simulated from the nonnal distribution and 5 nonnormal distributions. In addition, a new method of aligning two samples with unequal location parameters is proposed. This method shows significant improvement over aligning by either the median or …

Parametric Analyses In Randomized Clinical Trials, Vance W. Berger, Clifford E. Lunneborg, Michael D. Ernst, Jonathan G. Levine

Journal of Modern Applied Statistical Methods

One salient feature of randomized clinical trials is that patients are randomly allocated to treatment groups, but not randomly sampled from any target population. Without random sampling parametric analyses are inexact, yet they are still often used in clinical trials. Given the availability of an exact test, it would still be conceivable to argue convincingly that for technical reasons (upon which we elaborate) a parametric test might be preferable in some situations. Having acknowledged this possibility, we point out that such an argument cannot be convincing without supporting facts concerning the specifics of the problem at hand. Moreover, we have …

Nonparametric Confidence Intervals For The Reliability Of Real Systems Calculated From Component Data, Jean Spooner

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

A methodology which calculates a point estimate and confidence intervals for system reliability directly from component failure data is proposed and evaluated. This is a nonparametric approach which does not require the component time to failures to follow a known reliability distribution.

The proposed methods have similar accuracy to the traditional parametric approaches, can be used when the distribution of component reliability is unknown or there is a limited amount of sample component data, are simpler to compute, and use less computer resources. Depuy et al. (1982) studied several parametric approaches to calculating confidence intervals on system reliability. The test …

A Monte Carlo Comparison Of Nonparametric Reliability Estimators, Jia-Jinn Yueh

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

It is very difficult to construct a reliability model for a complex system. However, the reliability model for a series configuration is relatively simple. In the simplest case in which the components are mutually independent, the system reliability can be represented as follows:

R_s(x) = ∑ⁿ_i=1R_i(x),

where R_i is the reliability for the i^th component. It is also known that for moderate levels of system reliability for large systems, the component reliability must be high.

Extreme Value Theory indicates that under very general conditions, the initial form of the distribution function …

A Nonparametric Solution For Finding The Optimum Useful Life Of Equipment, Barry T. Stoll

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

It is often the case that equipment used by industry must be replaced with new equipment from time to time either because frequent malfunctions make it too costly to repair, or because the equipment has simply worn out. The new equipment often has the nature of either malfunctioning soon after installation due to manufacturing defects, or functioning for an extended period of time because it is free of these defects. For this reason, equipment is often given a preliminary running called the burn-in which gives no useful output but merely tests for manufacturing defects. Also, after a given amount of …

A Monte Carlo Evaluation Of A Nonparametric Technique For Estimating The Hazard Function, Sheng Jia Lin

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

This research is primarily concerned with the estimation of the Hazard functions, the Hazard function is the failure rate at time t, and is defined as -R '(t)/R(t), so it plays an important role in Reliability.

In order to compare and evaluate the estimation methods, it is convenient to select one distribution in this research. Since the Weibull distribution is a useful distribution in Reliability, the Weibull distribution is used in this paper.

Nonparametric Test Of Fit, Frena Nawabi

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

Most statistical methods require assumptions about the populations from which samples are taken. Usually these methods measure the parameters, such as variance, standard deviations, means, etc., of the respective populations. One example is the assumption that a given population can be approximated closely with a normal curve. Since these assumptions are not always valid, statisticians have developed several alternate techniques known as nonparametric tests. The models of such tests do not specify conditions about population parameters.

Certain assumptions, such as (1) observations are independent and (2) the variable being studied has underlying continuity, are associated with most nonparametric tests. However, …