Statistical Theory Commons^™

Robust Ancova: Confidence Intervals That Have Some Specified Simultaneous Probability Coverage When There Is Curvature And Two Covariates, Rand Wilcox

Journal of Modern Applied Statistical Methods

Consider the commonly occurring situation where the goal is to compare two independent groups and there are two covariates. Let Mj(X) be some conditional measure of location for the jth group associated with some random variable Y given X = (X1, X2). The goal is to H0: M1(X) = M2(X) for each X Ω in a manner that controls the probability of one or more Type I errors. An extant technique (method M1 here) addresses this goal without making any parametric assumption about Mj(X). However, a practical concern is that it does not provide enough detail regarding where the regression …

Limitations In The Systematic Analysis Of Structural Equation Model Fit Indices, Sarah A. Rose, Barry Markman, Shlomo Sawilowsky

Journal of Modern Applied Statistical Methods

The purpose of this study was to evaluate the sensitivity of selected fit index statistics in determining model fit in structural equation modeling (SEM). The results indicated a large dependency on correlation magnitude of the input correlation matrix, with mixed results when the correlation magnitudes were low and a primary indication of good model fit. This was due to the default SEM method of Maximum Likelihood that assumes unstandardized correlation values. However, this warning is not well-known, and is only obscurely mentioned in some textbooks. Many SEM computer software programs do not give appropriate error indications that the results are …

A Note On Determination Of Sample Size From The Perspective Of Six Sigma Quality, Joghee Ravichandran

Journal of Modern Applied Statistical Methods

In most empirical studies (clinical, network modeling, and survey-based and aeronautical studies, etc.), sample observations are drawn from population to analyze and draw inferences about the population. Such analysis is done with reference to a measurable quality characteristic of a product or process of interest. However, fixing a sample size is an important task that has to be decided by the experimenter. One of the means in deciding an appropriate sample size is the fixation of error limit and the associated confidence level. This implies that the analysis based on the sample used must guarantee the prefixed error and confidence …

Methodology For Constructing Perceptual Maps Incorporating Measuring Error In Sensory Acceptance Tests, Elisa Norberto Ferreira Santos, Gilberto Rodrigues Liska, Marcelo Angelo Cirillo

Journal of Modern Applied Statistical Methods

A new method is proposed based on construction of perceptual maps using techniques of correspondence analysis and interval algebra that allow specifying the measurement error expected in panel choices in the evaluation form described in unstructured 9-point hedonic scale.

Confidence Intervals For The Scaled Half-Logistic Distribution Under Progressive Type-Ii Censoring, Kiran Ganpati Potdar, D. T. Shirke

Journal of Modern Applied Statistical Methods

Confidence interval construction for the scale parameter of the half-logistic distribution is considered using four different methods. The first two are based on the asymptotic distribution of the maximum likelihood estimator (MLE) and log-transformed MLE. The last two are based on pivotal quantity and generalized pivotal quantity, respectively. The MLE for the scale parameter is obtained using the expectation-maximization (EM) algorithm. Performances are compared with the confidence intervals proposed by Balakrishnan and Asgharzadeh via coverage probabilities, length, and coverage-to-length ratio. Simulation results support the efficacy of the proposed approach.

A New Estimator Based On Auxiliary Information Through Quantitative Randomized Response Techniques, Nilgün Özgül, Hülya Çıngı

Journal of Modern Applied Statistical Methods

An exponential-type estimator is developed for the population mean of the sensitive study variable based on various Randomized Response Techniques (RRT) using a non-sensitive auxiliary variable. The mean squared error (MSE) of the proposed estimator is derived for generalized RRT models. The proposed estimator is compared with competitors in a simulation study and an application. The proposed estimator is found to be more efficient using a non-sensitive auxiliary variable.

Plant Leaf Image Detection Method Using A Midpoint Circle Algorithm For Shape-Based Feature Extraction, B. Vijaya Lakshmi, V. Mohan

Journal of Modern Applied Statistical Methods

Shape-based feature extraction in content-based image retrieval is an important research area at present. An algorithm is presented, based on shape features, to enhance the set of features useful in a leaf identification system.

Multiple Ratio Imputation By The Emb Algorithm: Theory And Simulation, Masayoshi Takahashi

Journal of Modern Applied Statistical Methods

Although multiple imputation is the gold standard of treating missing data, single ratio imputation is often used in practice. Based on Monte Carlo simulation, the Expectation-Maximization with Bootstrapping (EMB) algorithm to create multiple ratio imputation is used to fill in the gap between theory and practice.

Jmasm45: A Computer Program For Bayesian D-Optimal Binary Repeated Measurements Designs (Matlab), Haftom Temesgen Abebe, Frans E. S. Tan, Gerard J. P. Van Breukelen, Martijn P. F. Berger

Journal of Modern Applied Statistical Methods

Planners of longitudinal studies of binary responses in applied sciences have not yet benefitted from optimal designs, which have been shown to improve precision of model parameter estimates, due to absence of a computer program. An interactive computer program for Bayesian optimal binary repeated measurements designs is presented for this purpose.

An Extended Weighted Exponential Distribution, Abbas Mahdavi, Leila Jabari

Journal of Modern Applied Statistical Methods

A new class of weighted distributions is proposed by incorporating an extended exponential distribution in Azzalini’s (1985) method. Several statistics and reliability properties of this new class of distribution are obtained. Maximum likelihood estimators of the unknown parameters cannot be obtained in explicit forms; they have to be obtained by solving some numerical methods. Two data sets are analyzed for illustrative purposes, and show that the proposed model can be used effectively in analyzing real data.

A Comparison Of Depth Functions In Maximal Depth Classification Rules, Olusola Samuel Makinde, Adeyinka Damilare Adewumi

Journal of Modern Applied Statistical Methods

Data depth has been described as alternative to some parametric approaches in analyzing many multivariate data. Many depth functions have emerged over two decades and studied in literature. In this study, a nonparametric approach to classification based on notions of different data depth functions is considered and some properties of these methods are studied. The performance of different depth functions in maximal depth classifiers is investigated using simulation and real data with application to agricultural industry.

The Double Prior Selection For The Parameter Of Exponential Life Time Model Under Type Ii Censoring, Ronak M. Patel, Achyut C. Patel

Journal of Modern Applied Statistical Methods

A comparison of double informative priors assumed for the parameter of exponential life time model is considered. Three different sets of double priors are included, and the results are compared with a forth single prior. The data is Type II censored and Bayes estimators for the parameter and reliability are carried out under a squared error loss function in the cases of the four different sets of prior distributions. The predictive distribution was derived for future failure time and also for the remaining ordered failure times after the first r failure times have been observed. Corresponding Bayes credible equal tail …

Jmasm43: Teereg: Trimmed Elemental Estimation (R), Wei Jiang, Matthew S. Mayo

Journal of Modern Applied Statistical Methods

Trimmed elemental regression is robust to outliers and violations of model assumptions. Its properties and statistical inference were evaluated using bias-corrected and accelerated bootstrap confidence intervals. An R package named TEEReg is developed to compute the trimmed elemental estimates and the corresponding bootstrap confidence intervals. Two examples are provided to demonstrate its usage.

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.

Book Review: Multivariate Statistical Methods, A Primer, C. R. Rao

Journal of Modern Applied Statistical Methods

Multivariate Statistical Methods, A Primer, 4th Ed. Bryan F. J. Manly and Jorge A. Navarro Alberto. NY: Chapman & Hall / CRC Press. 2016. 264 p. ISBN 10: 1498728960 / ISBN 13: 978-1498728966

Jmasm44: Implementing Multiple Ratio Imputation By The Emb Algorithm (R), Masayoshi Takahashi

Journal of Modern Applied Statistical Methods

Although single ratio imputation is often used to deal with missing values in practice, there is a paucity of discussion regarding multiple ratio imputation. Code in the R statistical environment is presented to execute multiple ratio imputation by the Expectation-Maximization with Bootstrapping (EMB) algorithm.

Telephone Polls And Pps Sampling: A Potential Boon To The Polling Industry, Jade Mckay Burt

Undergraduate Honors Capstone Projects

In the wake of the 2016 election, the polling industry has no shortage of critics. While these are difficult times for the industry as a whole, there are exciting innovations happening that will serve to benefit and revitalize the industry for years. One of these exciting innovations is Probability Proportional to Size (PPS) sampling. I will elaborate on what PPS sampling is and provide a mathematical foundation for its use in polling. I also discuss what some of the myriad of issues plaguing the polling industry are and then show how PPS sampling can be used to remedy many of …

A Distribution Of The First Order Statistic When The Sample Size Is Random, Vincent Z. Forgo Mr

Electronic Theses and Dissertations

Statistical distributions also known as probability distributions are used to model a random experiment. Probability distributions consist of probability density functions (pdf) and cumulative density functions (cdf). Probability distributions are widely used in the area of engineering, actuarial science, computer science, biological science, physics, and other applicable areas of study. Statistics are used to draw conclusions about the population through probability models. Sample statistics such as the minimum, first quartile, median, third quartile, and maximum, referred to as the five-number summary, are examples of order statistics. The minimum and maximum observations are important in extreme value theory. This paper will …

Inference On The Stress-Strength Model From Weibull Gamma Distribution, Mahmoud Mansour, Rashad El-Sagheer, M. A. W. Mahmoud Prof.

Basic Science Engineering

No abstract provided.

High-Dimensional Repeated Measures, Martin Happ, Solomon W. Harrar, Arne C. Bathke

Statistics Faculty Publications

Recently, new tests for main and simple treatment effects, time effects, and treatment by time interactions in possibly high-dimensional multigroup repeated-measures designs with unequal covariance matrices have been proposed. Technical details for using more than one between-subject and more than one within-subject factor are presented in this article. Furthermore, application to electroencephalography (EEG) data of a neurological study with two whole-plot factors (diagnosis and sex) and two subplot factors (variable and region) is shown with the R package HRM (high-dimensional repeated measures).

Evaluation Of Progress Towards The Unaids 90-90-90 Hiv Care Cascade: A Description Of Statistical Methods Used In An Interim Analysis Of The Intervention Communities In The Search Study, Laura Balzer, Joshua Schwab, Mark J. Van Der Laan, Maya L. Petersen

U.C. Berkeley Division of Biostatistics Working Paper Series

WHO guidelines call for universal antiretroviral treatment, and UNAIDS has set a global target to virally suppress most HIV-positive individuals. Accurate estimates of population-level coverage at each step of the HIV care cascade (testing, treatment, and viral suppression) are needed to assess the effectiveness of "test and treat" strategies implemented to achieve this goal. The data available to inform such estimates, however, are susceptible to informative missingness: the number of HIV-positive individuals in a population is unknown; individuals tested for HIV may not be representative of those whom a testing intervention fails to reach, and HIV-positive individuals with a viral …

A Review Of The Multiple-Sample Tests For The Continuous-Data Type, Dewi Rahardja

Journal of Modern Applied Statistical Methods

For continuous data, various statistical hypotheses testing methods have been extensively discussed in the literature. In this article a review is provided of the multiple-sample continuous-data testing methods. It includes traditional methods, such as the two-sample t-test, Welch ANOVA test, etc., as well as newly-developed ones, such as the various Multiple Comparison Procedure (MCP). A roadmap is provided in a figure or diagram format as to which methods are available in the literature. Additionally, the implementation of these methods in popular statistical software packages such as SAS is also presented. This review will be helpful to determine which continuous-data testing …

Factor Analysis By Limited Scales: Which Factors To Analyze?, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Factor Analysis (FA) and Principal Component Analysis (PCA) are well-known main tools of the multivariate statistics for data analysis, reduction, and visualization. Commonly, the analysis and interpretation of their solutions is performed for each of several main eigenvectors with variances explaining a big part of the total variability in data. The recommendation is to determine if all the main vectors are really needed in the analysis, or some of them should be skipped if they correspond to the absence of the analyzing features. A simple criterion for identifying redundant vectors of loadings is their negative correlation with the vector of …

Prediction Of Percent Change In Linear Regression By Correlated Variables, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Multiple linear regression can be applied for predicting an individual value of dependent variable y by the given values of independent variables x. But it is not immediately clear how to estimate percent change in y due to changes in predictors, especially when those are correlated. This work considers several approaches to this problem, including its formulation via predictors adjusted by their correlation structure. Ordinary least squares regression is used, together with Shapley value regression and another model based on solving some system of differential equations. Numerical estimations performed for a real marketing research data demonstrate meaningful results. The considered …

Development And Properties Of Kernel-Based Methods For The Interpretation And Presentation Of Forensic Evidence, Douglas Armstrong

Electronic Theses and Dissertations

The inference of the source of forensic evidence is related to model selection. Many forms of evidence can only be represented by complex, high-dimensional random vectors and cannot be assigned a likelihood structure. A common approach to circumvent this is to measure the similarity between pairs of objects composing the evidence. Such methods are ad-hoc and unstable approaches to the judicial inference process. While these methods address the dimensionality issue they also engender dependencies between scores when 2 scores have 1 object in common that are not taken into account in these models. The model developed in this research captures …

An Empirical Demonstration Of The Need For Exact Tests, Vance W. Berger

Journal of Modern Applied Statistical Methods

The robustness of parametric analyses is rarely questioned or qualified. Robustness, generally understood, means the exact and approximate p-values will lie on the same side of alpha for any reasonable data set; and 1) any data set would qualify as reasonable and 2) robustness holds universally, for all alpha levels and approximations. For this to be true, the approximation would need to be perfect all of the time. Any discrepancy between the approximation and the exact p-value, for any combination of alpha level and data set, would constitute a violation. Clearly, this is not true, and when confronted with this …

Nonparametric Compound Estimation, Derivative Estimation, And Change Point Detection, Sisheng Liu

Theses and Dissertations--Statistics

Firstly, we reviewed some popular nonparameteric regression methods during the past several decades. Then we extended the compound estimation (Charnigo and Srinivasan [2011]) to adapt random design points and heteroskedasticity and proposed a modified Cp criteria for tuning parameter selection. Moreover, we developed a DCp criteria for tuning paramter selection problem in general nonparametric derivative estimation. This extends GCp criteria in Charnigo, Hall and Srinivasan [2011] with random design points and heteroskedasticity. Next, we proposed a change point detection method via compound estimation for both fixed design and random design case, the adaptation of heteroskedasticity was considered for the method. …

Informational Index And Its Applications In High Dimensional Data, Qingcong Yuan

Theses and Dissertations--Statistics

We introduce a new class of measures for testing independence between two random vectors, which uses expected difference of conditional and marginal characteristic functions. By choosing a particular weight function in the class, we propose a new index for measuring independence and study its property. Two empirical versions are developed, their properties, asymptotics, connection with existing measures and applications are discussed. Implementation and Monte Carlo results are also presented.

We propose a two-stage sufficient variable selections method based on the new index to deal with large p small n data. The method does not require model specification and especially focuses …

A New Approximation Scheme For Monte Carlo Applications, Bo Jones

CMC Senior Theses

Approximation algorithms employing Monte Carlo methods, across application domains, often require as a subroutine the estimation of the mean of a random variable with support on [0,1]. One wishes to estimate this mean to within a user-specified error, using as few samples from the simulated distribution as possible. In the case that the mean being estimated is small, one is then interested in controlling the relative error of the estimate. We introduce a new (epsilon, delta) relative error approximation scheme for [0,1] random variables and provide a comparison of this algorithm's performance to that of an existing approximation scheme, both …

Stochastic Optimization Of Adaptive Enrichment Designs For Two Subpopulations, Aaron Fisher, Michael Rosenblum

Johns Hopkins University, Dept. of Biostatistics Working Papers

An adaptive enrichment design is a randomized trial that allows enrollment criteria to be modified at interim analyses, based on a preset decision rule. When there is prior uncertainty regarding treatment effect heterogeneity, these trial designs can provide improved power for detecting treatment effects in subpopulations. We present a simulated annealing approach to search over the space of decision rules and other parameters for an adaptive enrichment design. The goal is to minimize the expected number enrolled or expected duration, while preserving the appropriate power and Type I error rate. We also explore the benefits of parallel computation in the …