Statistics and Probability Commons^™

Principal Component Preliminary Test Estimator In The Linear Regression Model, Sivarajah Arumairajan, Pushpakanthie Wijekoon

Journal of Modern Applied Statistical Methods

A Preliminary Test Estimator is introduced based on Principal Component Regression Estimator defined in the linear regression model when the stochastic restrictions are available in addition to the sample information, and when the explanatory variables are multicollinear. It is further developed as a large sample preliminary test estimator by using Wald (WA), Likelihood Ratio (LR), and Lagrangian Multiplier (LM) tests. Stochastic properties of this estimator based on F test as well as WA, LR, and LM tests are derived, and the performance of the estimator is compared using WA, LR, and LM tests with respect to Mean Square Error Matrix …

New Procedures Of Estimating Proportion And Sensitivity Using Randomized Response In A Dichotomous Finite Population, Tanveer A. Tarray, Housila P. Singh

Journal of Modern Applied Statistical Methods

The problem of estimating the population proportion possessing a sensitive attribute using simple random sampling with replacement (SRSWR) is advocated. Two new procedures are proposed. The suggested models are more efficient than the Huang (2004) randomized response technique under some realistic conditions. Numerical and graphic illustrations are given.

Construction Of Pair-Wise Balanced Design, Rajarathinam Arunachalam, Mahalakshmi Sivasubramanian, Dilip Kumar Ghosh

Journal of Modern Applied Statistical Methods

A new procedure for construction of pair wise balanced design with equal replication and un-equal block sizes based on factorial design have been evolved. Numerical illustration also provided. It was found that the constructed pair wise balanced design was found to be universal optimal.

The Eyes Have It: Eye Tracking Data Visualizations Of Viewing Patterns Of Statistical Graphics, Trent Fawcett

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

As statistical graphics continue to expand to manage an ever growing amount of diverse data, a need to evaluate the effectiveness of graphics, both basic and complex, has arisen. Technological advancements have given a means to evaluate the effectiveness of graphs and graphical components through eye tracking systems. Eye tracking systems are likewise in need of software that will enable easy evaluation and exploration of data. The focus of this Master's Report is to evaluate the dual solution. An exploration of an eye tracker setup is made, with extensive consideration of testing statistical graphics providing a basis for continued research …

Propensity Score Methods : A Simulation And Case Study Involving Breast Cancer Patients., John Craycroft

Electronic Theses and Dissertations

Observational data presents unique challenges for analysis that are not encountered with experimental data resulting from carefully designed randomized controlled trials. Selection bias and unbalanced treatment assignments can obscure estimations of treatment effects, making the process of causal inference from observational data highly problematic. In 1983, Paul Rosenbaum and Donald Rubin formalized an approach for analyzing observational data that adjusts treatment effect estimates for the set of non-treatment variables that are measured at baseline. The propensity score is the conditional probability of assignment to a treatment group given the covariates. Using this score, one may balance the covariates across treatment …

Generalized Linear Model Analyses For Treatment Group Equality When Data Are Non-Normal, Harvey J. Kesleman, Abdul R. Othman, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

One of the validity conditions of classical test statistics (e.g., Student’s t-test, the ANOVA and MANOVA F-tests) is that data be normally distributed in the populations. When this and/or other derivational assumptions do not hold the classical test statistic can be prone to too many Type I errors (i.e., falsely rejecting too often) and/or have low power (i.e., failing to reject when the null hypothesis is false) to detect treatment effects when they are present. However, alternative procedures are available for assessing equality of treatment group effects when data are non-normal. For example, researchers can use robust estimators …

Liu-Type Logistic Estimators With Optimal Shrinkage Parameter, Yasin Asar

Journal of Modern Applied Statistical Methods

Multicollinearity in logistic regression affects the variance of the maximum likelihood estimator negatively. In this study, Liu-type estimators are used to reduce the variance and overcome the multicollinearity by applying some existing ridge regression estimators to the case of logistic regression model. A Monte Carlo simulation is given to evaluate the performances of these estimators when the optimal shrinkage parameter is used in the Liu-type estimators, along with an application of real case data.

The Xgamma Distribution: Statistical Properties And Application, Subhradev Sen, Sudhansu S. Maiti, N. Chandra

Journal of Modern Applied Statistical Methods

A new probability distribution, the xgamma distribution, is proposed and studied. The distribution is generated as a special finite mixture of exponential and gamma distributions and hence the name proposed. Various mathematical, structural, and survival properties of the xgamma distribution are derived, and it is found that in many cases the xgamma has more flexibility than the exponential distribution. To evaluate the comparative behavior, stochastic ordering of the distribution is studied. To estimate the model parameter, the method of moment and the method of maximum likelihood estimation are proposed. A simulation algorithm to generate random samples from the xgamma distribution …

Analysis And Modeling Of Statistical Properties Of Fmdfb Subband Coefficients, E. Jebamalar Leavline, Sutha Shunmugam

Journal of Modern Applied Statistical Methods

Fast Multiscale Directional Filter Bank (FMDFB) is an image representation scheme used in several image processing applications. The statistical nature of the FMDFB subbands is analyzed, and a mathematical model of FMDFB coefficients is proposed. Experimental results are justified by goodness-of-fit tests.

Jmasm37: Simple Response Surface Methodology Using Rsreg (Sas), Wan Muhamad Amir, Mohamad Shafiq, Kasypi Mokhtar, Nor Azlida Aleng, Hanafi A.Rahim, Zalila Ali

Journal of Modern Applied Statistical Methods

Response surface methodology (RSM) can be used when the response variable, y, is influenced by several variables, x’s. When treatments take the form of quantitative values, then the true relationship between response variables and independent variables might be known. Examples are given in SAS.

Takens Theorem With Singular Spectrum Analysis Applied To Noisy Time Series, Thomas K. Torku

Electronic Theses and Dissertations

The evolution of big data has led to financial time series becoming increasingly complex, noisy, non-stationary and nonlinear. Takens theorem can be used to analyze and forecast nonlinear time series, but even small amounts of noise can hopelessly corrupt a Takens approach. In contrast, Singular Spectrum Analysis is an excellent tool for both forecasting and noise reduction. Fortunately, it is possible to combine the Takens approach with Singular Spectrum analysis (SSA), and in fact, estimation of key parameters in Takens theorem is performed with Singular Spectrum Analysis. In this thesis, we combine the denoising abilities of SSA with the Takens …

Generalized Singular Value Decomposition With Additive Components, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

The singular value decomposition (SVD) technique is extended to incorporate the additive components for approximation of a rectangular matrix by the outer products of vectors. While dual vectors of the regular SVD can be expressed one via linear transformation of the other, the modified SVD corresponds to the general linear transformation with the additive part. The method obtained can be related to the family of principal component and correspondence analyses, and can be reduced to an eigenproblem of a specific transformation of a data matrix. This technique is applied to constructing dual eigenvectors for data visualizing in a two dimensional …

Almost Unbiased Estimator Using Known Value Of Population Parameter(S) In Sample Surveys, Rajesh Singh, S.B. Gupta, Sachin Malik

Journal of Modern Applied Statistical Methods

An almost unbiased estimator using known value of some population parameter(s) is proposed. A class of estimators is defined which includes Singh and Solanki (2012) and Sahai and Ray (1980), Sisodiya and Dwivedi (1981), Singh, Cauhan, Sawan, and Smarandache (2007), Upadhyaya and Singh (1984), Singh and Tailor (2003) estimators. Under simple random sampling without replacement (SRSWOR) scheme the expressions for bias and mean square error (MSE) are derived. Numerical illustrations are given.

A Comparison Of Estimation Methods For Nonlinear Mixed-Effects Models Under Model Misspecification And Data Sparseness: A Simulation Study, Jeffrey R. Harring, Junhui Liu

Journal of Modern Applied Statistical Methods

A Monte Carlo simulation is employed to investigate the performance of five estimation methods of nonlinear mixed effects models in terms of parameter recovery and efficiency of both regression coefficients and variance/covariance parameters under varying levels of data sparseness and model misspecification.

Variable Selection In Regression Using Multilayer Feedforward Network, Tejaswi S. Kamble, Dattatraya N. Kashid

Journal of Modern Applied Statistical Methods

The selection of relevant variables in the model is one of the important problems in regression analysis. Recently, a few methods were developed based on a model free approach. A multilayer feedforward neural network model was proposed for developing variable selection in regression. A simulation study and real data were used for evaluating the performance of proposed method in the presence of outliers, and multicollinearity.

Jmasm39: Algorithm For Combining Robust And Bootstrap In Multiple Linear Model Regression (Sas), Wan Muhamad Amir, Mohamad Shafiq, Hanafi A.Rahim, Puspa Liza, Azlida Aleng, Zailani Abdullah

Journal of Modern Applied Statistical Methods

The aim of bootstrapping is to approximate the sampling distribution of some estimator. An algorithm for combining method is given in SAS, along with applications and visualizations.

Jmasm35: A Percentile-Based Power Method: Simulating Multivariate Non-Normal Continuous Distributions (Sas), Jennifer Koran, Todd C. Headrick

Journal of Modern Applied Statistical Methods

The conventional power method transformation is a moment-matching technique that simulates non-normal distributions with controlled measures of skew and kurtosis. The percentile-based power method is an alternative that uses the percentiles of a distribution in lieu of moments. This article presents a SAS/IML macro that implements the percentile-based power method.

New Flexible Regression Models Generated By Gamma Random Variables With Censored Data, Elizabeth M. Hashimoto, Gauss M. Cordeiro, Edwin M. M. Ortega, Gholamhossein G. Hamedani

Mathematics, Statistics and Computer Science Faculty Research and Publications

We propose and study a new log-gamma Weibull regression model. We obtain explicit expressions for the raw and incomplete moments, quantile and generating functions and mean deviations of the log-gamma Weibull distribution. We demonstrate that the new regression model can be applied to censored data since it represents a parametric family of models which includes as sub-models several widely-known regression models and therefore can be used more effectively in the analysis of survival data. We obtain the maximum likelihood estimates of the model parameters by considering censored data and evaluate local influence on the estimates of the parameters by taking …

Self-Monitoring Practices, Attitudes, And Needs Of Individuals With Bipolar Disorder: Implications For The Design Of Technologies To Manage Mental Health, Elizabeth L. Murnane, Dan Cosley, Pamara Chang, Shion Guha, Ellen Frank, Geri K. Gay, Mark Matthews

Mathematics, Statistics and Computer Science Faculty Research and Publications

Objective To understand self-monitoring strategies used independently of clinical treatment by individuals with bipolar disorder (BD), in order to recommend technology design principles to support mental health management.

Materials and Methods Participants with BD (N = 552) were recruited through the Depression and Bipolar Support Alliance, the International Bipolar Foundation, and WeSearchTogether.org to complete a survey of closed- and open-ended questions. In this study, we focus on descriptive results and qualitative analyses.

Results Individuals reported primarily self-monitoring items related to their bipolar disorder (mood, sleep, finances, exercise, and social interactions), with an increasing trend towards the use of digital …

Risk Estimation Toward A Natural History Model For Low Grade Glioma Patients, Anh Thi Hoang Pham

Graduate Theses and Dissertations

Glioma is a common type of primary brain tumor that represents 28% of all brain tumors and 80% of malignant tumors. According to a recent study by the Centers for Disease Control and Prevention (CDC), gliomas account for 53%, 35% and 29% of all brain tumors (68%, 74% and 81% of malignant brain tumors) among children (aged 0-14), teenagers (aged 15-19) and young adults, respectively. Gliomas are often diagnosed through radiological imaging and histopathology. There are two main groups of gliomas following World Health Organization’s classification: Low grade gliomas (LGG), or grade I and II gliomas; and high grade gliomas …