Statistical Theory Commons^™

Estimation For The Parameters Of The Exponentiated Exponential Distribution Using A Median Ranked Set Sampling, Monjed H. Samuh, Areen Qtait

Journal of Modern Applied Statistical Methods

The method of maximum likelihood estimation based on Median Ranked Set Sampling (MRSS) was used to estimate the shape and scale parameters of the Exponentiated Exponential Distribution (EED). They were compared with the conventional estimators. The relative efficiency was used for comparison. The amount of information (in Fisher's sense) available from the MRSS about the parameters of the EED were be evaluated. Confidence intervals for the parameters were constructed using MRSS.

Estimating The Strength Of An Association Based On A Robust Smoother, Rand Wilcox

Journal of Modern Applied Statistical Methods

It is known that the more obvious parametric approaches to fitting a regression line to data are often not flexible enough to provide an adequate approximation of the true regression line. Many nonparametric regression estimators, often called smoothers, have been derived that are aimed at dealing with this problem. The paper deals with the issue of estimating the strength of an association based on the fit obtained by a robust smoother. A simple approach, already known, is to estimate explanatory power in a fairly obvious manner. This approach has been found to perform reasonably well when using the smoother LOESS. …

Per Family Or Familywise Type I Error Control: "Eether, Eyether, Neether, Nyther, Let's Call The Whole Thing Off!", H. J. Keselman

Journal of Modern Applied Statistical Methods

Frane (2015) pointed out the difference between per-family and familywise Type I error control and how different multiple comparison procedures control one method but not necessarily the other. He then went on to demonstrate in the context of a two group multivariate design containing different numbers of dependent variables and correlations between variables how the per-family rate inflates beyond the level of significance. In this article I reintroduce other newer better methods of Type I error control. These newer methods provide more power to detect effects than the per-family and familywise techniques of control yet maintain the overall rate of …

Comparison Of Bayesian Credible Intervals To Frequentist Confidence Intervals, Kathy Gray, Brittany Hampton, Tony Silveti-Falls, Allison Mcconnell, Casey Bausell

Journal of Modern Applied Statistical Methods

Frequentist confidence intervals were compared with Bayesian credible intervals under a variety of scenarios to determine when Bayesian credible intervals outperform frequentist confidence intervals. Results indicated that Bayesian interval estimation frequently produces results with precision greater than or equal to the frequentist method.

Special Education Distributions And Analysis, Valerie Felder, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

Micceri (1989) examined the distributional characteristics of 440 large sample general education achievement and psychometric measures. All the distributions were found to be statistically significantly different from the normal distribution. In this study, 395 special education datasets were examined. Although there were some normally distributed datasets, most were not, and some were markedly different in shape from those found by Micceri (1989). Implications for statistical testing and making special education policy decisions were given.

Vol. 14, No. 1 (Full Issue), Jmasm Editors

Journal of Modern Applied Statistical Methods

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A Comparison Of Semi-Parametric And Nonparametric Methods For Estimating Mean Time To Event For Randomly Left Censored Data, Farzana Chowdhury, Jahida Gulshan, Syed Shahadat Hossain

Journal of Modern Applied Statistical Methods

The aim of this study was to make a comparison among existing estimation methods (Kaplan-Meier, Nelson-Aalen and Regression on Ordered Statistics (ROS)) for randomly left censored time to event data under selected distributions and for different level of censoring and sample sizes in order to determine the strength of these methods based on simulated data. Comparisons among the methods are made on the basis of unbiasedness and Monte Carlo Standard Error of the summary statistics (mean time to event) obtained by those methods under different conditions.

Bootstrapping Vs. Asymptotic Theory In Property And Casualty Loss Reserving, Andrew J. Difronzo Jr.

Honors Projects in Mathematics

One of the key functions of a property and casualty (P&C) insurance company is loss reserving, which calculates how much money the company should retain in order to pay out future claims. Most P&C insurance companies use non-stochastic (non-random) methods to estimate these future liabilities. However, future loss data can also be projected using generalized linear models (GLMs) and stochastic simulation. Two simulation methods that will be the focus of this project are: bootstrapping methodology, which resamples the original loss data (creating pseudo-data in the process) and fits the GLM parameters based on the new data to estimate the sampling …

Best Practice Recommendations For Data Screening, Justin A. Desimone, Peter D. Harms, Alice J. Desimone

Department of Management: Faculty Publications

Survey respondents differ in their levels of attention and effort when responding to items. There are a number of methods researchers may use to identify respondents who fail to exert sufficient effort in order to increase the rigor of analysis and enhance the trustworthiness of study results. Screening techniques are organized into three general categories, which differ in impact on survey design and potential respondent awareness. Assumptions and considerations regarding appropriate use of screening techniques are discussed along with descriptions of each technique. The utility of each screening technique is a function of survey design and administration. Each technique has …

A Generalized Inflated Geometric Distribution, Ram Datt Joshi

Theses, Dissertations and Capstones

A count data that have excess number of zeros, ones, twos or threes are commonplace in experimental studies. But these inflated frequencies at particular counts may lead to over dispersion and thus may cause difficulty in data analysis. So, to get appropriate results from them and to overcome the possible anomalies in parameter estimation, we may need to consider suitable inflated distribution.

In this thesis, we have considered a Swedish fertility dataset with inflated values at some particular counts. Generally, Inflated Poisson or Inflated Negative Binomial distribution are the most common distributions for analyzing such data. Geometric distribution can be …

Statistical Inference For The Mean Outcome Under A Possibly Non-Unique Optimal Treatment Strategy, Alexander R. Luedtke, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

We consider challenges that arise in the estimation of the value of an optimal individualized treatment strategy defined as the treatment rule that maximizes the population mean outcome, where the candidate treatment rules are restricted to depend on baseline covariates. We prove a necessary and sufficient condition for the pathwise differentiability of the optimal value, a key condition needed to develop a regular asymptotically linear (RAL) estimator of this parameter. The stated condition is slightly more general than the previous condition implied in the literature. We then describe an approach to obtain root-n rate confidence intervals for the optimal value …

Higher-Order Targeted Minimum Loss-Based Estimation, Marco Carone, Iván Díaz, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Common approaches to parametric statistical inference often encounter difficulties in the context of infinite-dimensional models. The framework of targeted maximum likelihood estimation (TMLE), introduced in van der Laan & Rubin (2006), is a principled approach for constructing asymptotically linear and efficient substitution estimators in rich infinite-dimensional models. The mechanics of TMLE hinge upon first-order approximations of the parameter of interest as a mapping on the space of probability distributions. For such approximations to hold, a second-order remainder term must tend to zero sufficiently fast. In practice, this means an initial estimator of the underlying data-generating distribution with a sufficiently large …

Retained-Components Factor Transformation: Factor Loadings And Factor Score Predictors In The Column Space Of Retained Components, André Beauducel, Frank Spohn

Journal of Modern Applied Statistical Methods

Factor loadings optimally account for the non-diagonal elements of the covariance matrix of observed variables. Principal component analysis leads to components accounting for a maximum of the variance of the observed variables. Retained-components factor transformation is proposed in order to combine the advantages of factor analysis and principal component analysis.

Pairwise Comparison In Repeated Measures, I.C.A. Oyeka, C. C. Nnanatu

Journal of Modern Applied Statistical Methods

Sometimes a random sample of subjects or patients may be exposed to a battery of diagnostic tests or medication over time and interest is on determining whether there is progressive remission of condition, disease or symptom. Also perhaps early in a program or experiment, subjects or candidates may be required to significantly improve in their performance rates at the current trial relative to an immediately preceding trial, otherwise they may have to withdraw from or drop out. The research interest would then be to determine some critical minimum marginal success rate to guide the management in decision making as well …

A Comparison Of Methods For Group Prediction With High Dimensional Data, Holmes Finch

Journal of Modern Applied Statistical Methods

High dimensional data is the situation in which the number of variables included in an analysis approaches or exceeds the sample size. In the context of group classification, researchers are typically interested in finding a model that can be used to correctly place an individual into their appropriate group; e.g. correctly diagnose individuals with depression. However, when the size of the training sample is small and the number of predictors used to differentiate the groups is larger, standard approaches such as discriminant analysis may not work well. In order to address this issue, statisticians have developed a number of tools …

Objective Priors For Estimation Of Extended Exponential Geometric Distribution, Pedro L. Ramos, Fernando A. Moala, Jorge A. Achcar

Journal of Modern Applied Statistical Methods

A Bayesian analysis was developed with different noninformative prior distributions such as Jeffreys, Maximal Data Information, and Reference. The aim was to investigate the effects of each prior distribution on the posterior estimates of the parameters of the extended exponential geometric distribution, based on simulated data and a real application.

Some General Guidelines For Choosing Missing Data Handling Methods In Educational Research, Jehanzeb R. Cheema

Journal of Modern Applied Statistical Methods

The effect of a number of factors, such as the choice of analytical method, the handling method for missing data, sample size, and proportion of missing data, were examined to evaluate the effect of missing data treatment on accuracy of estimation. A methodological approach involving simulated data was adopted. One outcome of the statistical analyses undertaken in this study is the formulation of easy-to-implement guidelines for educational researchers that allows one to choose one of the following factors when all others are given: sample size, proportion of missing data in the sample, method of analysis, and missing data handling method.

Bayesian Inference For Volatility Of Stock Prices, Juliet G. D'Cunha, K. A. Rao

Journal of Modern Applied Statistical Methods

Lognormal distribution is widely used in the analysis of failure time data and stock prices. Maximum likelihood and Bayes estimator of the coefficient of variation of lognormal distribution along with confidence/credible intervals are developed. The utility of Bayes procedure is illustrated by analyzing prices of selected stocks.

Local Bandwidths For Improving Performance Statistics Of Model-Robust Regression 2, Efosa Edionwe, Julian L. Mbegbu

Journal of Modern Applied Statistical Methods

Model-Robust Regression 2 (MRR2) method is a semi-parametric regression approach that combines parametric and nonparametric fits. The bandwidth controls the smoothness of the nonparametric portion. We present a methodology for deriving data-driven local bandwidth that enhances the performance of MRR2 method for fitting curves to data generated from designed experiments.

Contrast Of Bayesian And Classical Sample Size Determination, Farhana Sadia, Syed S. Hossain

Journal of Modern Applied Statistical Methods

Sample size determination is a prerequisite for statistical surveys. A comprehensive overview of the Bayesian approach for computation of the sample size, and a comparison with classical approaches, is presented. Two surveys are taken as example to illustrate the accuracy and efficiency of each approach, and to make recommendations about which method is preferred. The Bayesian approach of sample size determination may require fewer subjects if proper prior information is available.