Statistical Theory Commons^™

An Extension Of Cochran-Orcutt Procedure For Generalized Linear Regression Models With Periodically Correlated Errors, Abdullah A. Smadi, Nour H. Abu-Afouna

Journal of Modern Applied Statistical Methods

An important assumption of ordinary regression models is independence among errors. This research considers the case of periodically correlated errors following the periodic AR model of order 1 (PAR(1)). The remedial measure for correlated errors in regression known as the Cochran-Orcutt procedure is generalized to the case of periodically correlated errors. The motivation for making such generalizations is that the response data may inhibit some seasonality, which may not be captured by the traditional AR(1) autoregressive model. The proposed procedure is described and the bias and MSE of the resulting intercept and slope parameter estimates of the simple LR model …

A Proposed Ridge Parameter To Improve The Least Square Estimator, Ghadban Khalaf

Journal of Modern Applied Statistical Methods

Ridge regression, a form of biased linear estimation, is a more appropriate technique than ordinary least squares (OLS) estimation in the case of highly intercorrelated explanatory variables in the linear regression model Y = β + u. Two proposed ridge regression parameters from the mean square error (MSE) perspective are evaluated. A simulation study was conducted to demonstrate the performance of the proposed estimators compared to the OLS, HK and HKB estimators. Results show that the suggested estimators outperform the OLS and the other estimators regarding the ridge parameters in all situations examined.

Graphical Modeling For High Dimensional Data, Munni Begum, Jay Bagga, C. Ann Blakey

Journal of Modern Applied Statistical Methods

With advances in science and information technologies, many scientific fields are able to meet the challenges of managing and analyzing high-dimensional data. A so-called large p small n problem arises when the number of experimental units, n, is equal to or smaller than the number of features, p. A methodology based on probability and graph theory, termed graphical models, is applied to study the structure and inference of such high-dimensional data.

A Graphical Examination Of Variable Deletion Within The Mewma Statistic, Jay R. Schaffer, Shawn Vandenhul

Journal of Modern Applied Statistical Methods

A general procedure for identifying the variable(s) that contribute(s) to the signal of the multivariate extension of the exponentially weighted moving average (MEWMA) chart is presented. The procedure systematically removes one or two variables from the MEWMA statistic calculations. Percentages are calculated for correctly identifying various shifts.

Testing The Population Coefficient Of Variation, Shipra Banik, B. M. Golam Kibria, Dinesh Sharma

Journal of Modern Applied Statistical Methods

The coefficient of variation (CV), which is used in many scientific areas, measures the variability of a population relative to its mean and standard deviation. Several methods exist for testing the population CV. This article compares a proposed bootstrap method to existing methods. A simulation study was conducted under both symmetric and skewed distributions to compare the performance of test statistics with respect to empirical size and power. Results indicate that some of the proposed methods are useful and can be recommended to practitioners.

Bayesian Estimation Of Erlang Distribution Under Different Generalized Truncated Distributions As Priors, Adil H. Khan, T.R. Jan

Journal of Modern Applied Statistical Methods

Various generalized truncated distributions are considered as independent informative priors for estimating shape and scale parameters of the Erlang distribution. In addition, various special cases are also discussed.

Multivariate Generalized Poisson Distribution For Interference On Selected Non-Communicable Diseases In Lagos State, Nigeria, Adewara Johnson Ademola, Mbata Ugochuckwu Ahamefula

Journal of Modern Applied Statistical Methods

Multivariate Generalized Poisson Distribution (MGPD) models are applied to make inferences regarding non-communicable diseases, diabetes, hypertension, stroke and ulcer in Lagos State, Nigeria. The generalized Poisson distribution is employed due to its usefulness in modeling count data in the presence of either over- or under- dispersion. Results show that the correlation between ulcer and stroke is not significant. Other pairwise comparisons of diseases are significant, thus implying that a patient who suffers from diabetes or stroke has a high propensity to also be hypertensive.

Ferrieri's Index Of Openness Applied To Remittances To Developing Countries, Gaetano Ferrieri

Journal of Modern Applied Statistical Methods

A new methodology to measure international openness and globalization is described. This allows capacity to be effectively combined with size in a number of socio-economic areas, such as trade, migration and foreign investment. The method is applied to remittances to developing countries.

Finding A Better Confidence Interval For A Single Regression Changepoint Using Different Bootstrap Confidence Interval Procedures, Bodhipaksha Thilakarathne

College of Graduate Studies: Theses & Dissertations

Recently a number of papers have been published in the area of regression changepoints but there is not much literature concerning confidence intervals for regression changepoints. The purpose of this paper is to find a better bootstrap confidence interval for a single regression changepoint. ("Better" confidence interval means having a minimum length and coverage probability which is close to a chosen significance level). Several methods will be used to find bootstrap confidence intervals. Among those methods a better confidence interval will be presented.

A Prior-Free Framework Of Coherent Inference And Its Derivation Of Simple Shrinkage Estimators, David R. Bickel

COBRA Preprint Series

The reasoning behind uses of confidence intervals and p-values in scientific practice may be made coherent by modeling the inferring statistician or scientist as an idealized intelligent agent. With other things equal, such an agent regards a hypothesis coinciding with a confidence interval of a higher confidence level as more certain than a hypothesis coinciding with a confidence interval of a lower confidence level. The agent uses different methods of confidence intervals conditional on what information is available. The coherence requirement means all levels of certainty of hypotheses about the parameter agree with the same distribution of certainty over parameter …

Foundations Of Inference, Kevin H. Knuth, John Skilling

Physics Faculty Scholarship

We present a simple and clear foundation for finite inference that unites and significantly extends the approaches of Kolmogorov and Cox. Our approach is based on quantifying lattices of logical statements in a way that satisfies general lattice symmetries. With other applications such as measure theory in mind, our derivations assume minimal symmetries, relying on neither negation nor continuity nor differentiability. Each relevant symmetry corresponds to an axiom of quantification, and these axioms are used to derive a unique set of quantifying rules that form the familiar probability calculus. We also derive a unique quantification of divergence, entropy and information.

Adaptive Randomization Designs, Jenna Colavincenzo

Statistics

Adaptive design methodologies use prior information to develop a clinical trial design. The goal of an adaptive design is to maintain the integrity and validity of the study while giving the researcher flexibility in identifying the optimal treatment. An example of an adaptive design can be seen in a basic pharmaceutical trial. There are three phases of the overall trial to compare treatments and experimenters use the information from the previous phase to make changes to the subsequent phase before it begins.

Adaptive design methods have been in practice since the 1970s, but have become increasingly complex ever since. One …

Rank-Based Estimation And Prediction For Mixed Effects Models In Nested Designs, Yusuf K. Bilgic

Dissertations

Hierarchical designs frequently occur in many research areas. The experimental design of interest is expressed in terms of fixed effects but, for these designs, nested factors are a natural part of the experiment. These nested effects are generally considered random and must be taken into account in the statistical analysis. Traditional analyses are quite sensitive to outliers and lose considerable power to detect the fixed effects of interest.

This work proposes three rank-based fitting methods for handling random, fixed and scale effects in k-level nested designs for estimation and inference. An algorithm, which iteratively obtains robust prediction for both scale …

Bayesian And Related Methods: Techniques Based On Bayes' Theorem, Mehmet Vurkaç

Systems Science Friday Noon Seminar Series

Bayes' theorem is a simple algebraic consequence of conditional probability. Yet, its consequences are critical to philosophy, society, and technology. Starting from its simple derivation, we will show how its interpretation in terms of base rates (priors) and class-conditional likelihoods illuminates everyday problems in medicine and law, and provides signal processing, communications, machine learning, model selection, and other applications of statistics with powerful classification and estimation tools. Next, we will briefly examine some of the ways in which this theorem can be adopted to include multiple attributes, contexts, hypotheses, and levels of risk. Methods derived from or related to Bayes’ …

Confidence Intervals For The Selected Population In Randomized Trials That Adapt The Population Enrolled, Michael Rosenblum

Johns Hopkins University, Dept. of Biostatistics Working Papers

It is a challenge to design randomized trials when it is suspected that a treatment may benefit only certain subsets of the target population. In such situations, trial designs have been proposed that modify the population enrolled based on an interim analysis, in a preplanned manner. For example, if there is early evidence that the treatment only benefits a certain subset of the population, enrollment may then be restricted to this subset. At the end of such a trial, it is desirable to draw inferences about the selected population. We focus on constructing confidence intervals for the average treatment effect …

The Impact Of Violating Factor Scaling Method Assumptions On Latent Mean Difference Testing In Structured Means Models, Dandan Wang, Tiffany A. Whittaker, S. Natasha Beretvas

Journal of Modern Applied Statistical Methods

Type I error rates and power of the likelihood ratio test and bias of the standardized effect size measure associated with the latent mean difference in structured means modeling are examined when violating the assumptions underlying the two available factor scaling methods under various conditions. Implications and recommendations are discussed.

New Approximate Bayesian Confidence Intervals For The Coefficient Of Variation Of A Gaussian Distribution, Vincent A. R. Camara

Journal of Modern Applied Statistical Methods

Confidence intervals are constructed for the coefficient of variation of a Gaussian distribution. Considering the square error and the Higgins-Tsokos loss functions, approximate Bayesian models are derived and compared to a published classical model. The models are shown to have great coverage accuracy. The classical model does not always yield the best confidence intervals; the proposed models often perform better.

A Poisson Regression Model For Female Radium Dial Workers, Tze-San Lee

Journal of Modern Applied Statistical Methods

A Poisson regression model with interaction terms was applied to study the dose response relationship for radium-induced skeletal cancers. The model showed that the expected frequency count of bone tumors depended not only on the logarithmic dose and the time since first exposure, but also on the interaction between the logarithmic dose and the time since first exposure, whereas the dose-response model for head tumors depended only on the logarithmic dose.

Jmasm 32: Sas Template For Single-Subject Experimental Designs, Hyewon Chung, Jiseon Kim, Ryoungsun Park

Journal of Modern Applied Statistical Methods

Meta-analysis has been used to synthesize research findings and to evaluate the effectiveness of treatments or the accuracy of diagnostic tools. Although meta-analytic techniques were developed to synthesize the results of several studies, controversy exists as to how to quantify the results from singlesubject experimental designs (SSEDs). The most commonly used metrics are reviewed, including nonregression and regression based methods. The application of the SAS template is demonstrated through simulated data sets. The SAS templates can be modified to accommodate a more complex data structure.

The Length-Biased Lognormal Distribution And Its Application In The Analysis Of Data From Oil Field Exploration Studies, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar

Journal of Modern Applied Statistical Methods

The length-biased version of the lognormal distribution and related estimation problems are considered and sized-biased data arising in the exploration of oil fields is analyzed. The properties of the estimators are studied using simulations and the use of sample mode as an estimate of the lognormal parameter is discussed.

Four Period Crossover Designs, James F. Reed Iii

Journal of Modern Applied Statistical Methods

In higher-order four period crossover designs with two treatments, sixteen possible treatment sequences can result: AAAA, AAAB, AABA, AABB, ABAA, ABAB, ABBA, ABBB and their duals. Higher-order crossover designs are useful for several reasons: they allow estimation of a treatment effect even in the presence of a carry-over effect, they provide estimates of intra-subject variability and they draw inference on the carry-over effect. The real question related to a two-treatment four-period crossover design is the real world application of these designs. This article considers four designs: Design I: ABBA and its dual; Design II: ABBA, AABB and their duals, Design …

Gamma-Pareto Distribution And Its Applications, Ayman Alzaatreh, Felix Famoye, Carl Lee

Journal of Modern Applied Statistical Methods

A new distribution, the gamma-Pareto, is defined and studied and various properties of the distribution are obtained. Results for moments, limiting behavior and entropies are provided. The method of maximum likelihood is proposed for estimating the parameters and the distribution is applied to fit three real data sets.

A Weighted Exponential Detection Function Model For Line Transect Data, Faisal Ababneh, Omar M. Eidous

Journal of Modern Applied Statistical Methods

A new parametric model is proposed for modeling the density function of perpendicular distances in line transects sampling. The model can be considered a weighted exponential model in the sense that it combines two exponential models with different weights. The proposed model is appealing because it is monotone decreasing with distance from transect line; in contrast to the classical exponential model, it satisfies the shoulder condition at the origin. Simulation results for a wide range of target densities show reasonable and good performances of the weighted exponential model in most considered cases compared to the classical exponential and the half-normal …

Ordinal Regression Analysis: Using Generalized Ordinal Logistic Regression Models To Estimate Educational Data, Xing Liu, Hari Koirala

Journal of Modern Applied Statistical Methods

The proportional odds (PO) assumption for ordinal regression analysis is often violated because it is strongly affected by sample size and the number of covariate patterns. To address this issue, the partial proportional odds (PPO) model and the generalized ordinal logit model were developed. However, these models are not typically used in research. One likely reason for this is the restriction of current statistical software packages: SPSS cannot perform the generalized ordinal logit model analysis and SAS requires data restructuring. This article illustrates the use of generalized ordinal logistic regression models to predict mathematics proficiency levels using Stata and compares …

Robust Regression Estimates In The Prediction Of Latent Variables In Structural Equation Models, Marcelo Angelo Cirillo, Lúcia Pereira Barroso

Journal of Modern Applied Statistical Methods

The incorporation of the robust regression methods Least Median Square (LMS) and Least Trimmed Squares (LTS) is proposed in structural equation modeling. Results show that, in situations of high deviations of symmetry, the evaluated methods would be recommended for applications including smaller sample sizes.

Comparison Of Re-Sampling Methods To Generalized Linear Models And Transformations In Factorial And Fractional Factorial Designs, Maher Qumsiyeh, Gerald Shaughnessy

Journal of Modern Applied Statistical Methods

Experimental situations in which observations are not normally distributed frequently occur in practice. A common situation occurs when responses are discrete in nature, for example counts. One way to analyze such experimental data is to use a transformation for the responses; another is to use a link function based on a generalized linear model (GLM) approach. Re-sampling is employed as an alternative method to analyze non-normal, discrete data. Results are compared to those obtained by the previous two methods.

Statistical Inferences For Lomax Distribution Based On Record Values (Bayesian And Classical), Parviz Nasiri, Saman Hosseini

Journal of Modern Applied Statistical Methods

A maximum likelihood estimation (MLE) based on records is obtained and a proper prior distribution to attain a Bayes estimation (both informative and non-informative) based on records for quadratic loss and squared error loss functions is also calculated. The study considers the shortest confidence interval and Highest Posterior Distribution confidence interval based on records, and using Mean Square Error MSE criteria for point estimation and length criteria for interval estimation, their appropriateness to each other is examined.

Empirical Sampling From Permutation Space With Unique Patterns, Justice I. Odiase

Journal of Modern Applied Statistical Methods

The exact distribution of a test statistic ultimately guarantees that the probability of a Type I error is exactly α. Several methods for estimating the exact distribution of a test statistic have evolved over the years with inherent computational problems and varying degrees of accuracy. The unique pattern of permutations resulting from using experimental data to sample within the permutation space without the risk of repeating permutations is identified. The method presented circumvents the theoretical requirements of asymptotic procedures and the computational difficulties associated with an exhaustive enumeration of permutations. Results show that time and space complexities are drastically reduced …

Weight: Does It Really Matter?, Jennifer L. Brown, Gerald Halpin, Glennelle Halpin

Journal of Modern Applied Statistical Methods

Differential weighting promises to improve the validity of a measure. This study examines whether similar results would be found using weighted, unweighted and standardized z scores from the All Stars Core survey. It was concluded that the weighted systems were developed to equate the questions within the scales and to ease the process for customers without access to data analysis programs; however, the standardized scores were the more appropriate method for equating the test items.

Ratio Type Estimator Of Ratio Of Two Population Means In Stratified Random Sampling, Rajesh Tailor, Sunil Chouhan

Journal of Modern Applied Statistical Methods

A ratio estimator is proposed for the ratio of two population means using auxiliary information in stratified random sampling. Bias and mean squared error expressions are obtained under large sample approximation, and the proposed estimator is compared both theoretically and empirically with the conventional estimator of ratio for two population means in stratified random sampling.