Statistical Theory Commons^™

Rao-Lovric And The Triwizard Point Null Hypothesis Tournament, Shlomo Sawilowsky

Journal of Modern Applied Statistical Methods

The debate if the point null hypothesis is ever literally true cannot be resolved, because there are three competing statistical systems claiming ownership of the construct. The local resolution depends on personal acclimatization to a Fisherian, Frequentist, or Bayesian orientation (or an unexpected fourth champion if decision theory is allowed to compete). Implications of Rao and Lovric’s proposed Hodges-Lehman paradigm are discussed in the Appendix.

Estimation Of Population Mean On Recent Occasion Under Non-Response In H-Occasion Successive Sampling, Anup Kumar Sharma, Garib Nath Singh

Journal of Modern Applied Statistical Methods

In this article, an attempt has been made to study on general estimation procedures of population mean on recent occasion when non-response occurs in h-occasion successive sampling. Suggested estimators have advantageously influenced the estimation procedures in the presence of non-response. Detailed properties of the suggested estimation procedures have been examined and compared with the estimation process of the same circumstances but in the absence of non-response. Empirical studies have been carried out to demonstrate the performances of the estimates and suitable recommendations have been made.

Vol. 15, No. 2 (Full Issue), Jmasm Editors

Journal of Modern Applied Statistical Methods

.

An Improved Generalized Estimation Procedure Of Current Population Mean In Two-Occasion Successive Sampling, G. N. Singh, Alok Kumar Singh, Anup Kumar Sharma

Journal of Modern Applied Statistical Methods

The present work is an attempt to make use of several auxiliary variables on both occasions for improving the precision of estimates for the current population mean in two-occasion successive sampling. A generalized exponential-cum-regression type estimator of the current population mean is proposed and its optimum replacement strategy has been discussed. Empirical studies are carried out to show the dominance of the proposed estimation procedure over the sample mean estimator and natural successive sampling estimator. Empirical results have been interpreted and suitable recommendations are put forward to survey practitioners.

A Comprehensive Review Of The Two-Sample Independent Or Paired Binary Data, With Or Without Stratum Effects, Dewi Rahardja, Ying Yang, Zhiwei Zhang

Journal of Modern Applied Statistical Methods

Various statistical hypotheses testing for discrete or categorical or binary data have been extensively discussed in the literature. A comprehensive review is given for the two-sample binary or categorical data testing methods on data with or without Stratum Effects. The review includes traditional methods such as Fisher’s Exact, Pearson’s Chi-Square, McNemar, Bowker, Stuart-Maxwell, Breslow-Day and, Cochran-Mantel-Haenszel, as well as newly developed ones. We also provide the roadmap, in a figure or diagram format to which methods are available in the literature. In addition, the implementation of these methods in popular statistical software packages such as SAS and/or R is also …

Evaluation Of The Addition Of Firth’S Penalty Term To The Bradley-Terry Likelihood, Paul Meyvisch

Journal of Modern Applied Statistical Methods

A major shortcoming of the Bradley-Terry model is that the maximum likelihood estimates are infinite-valued in the presence of separation and may be unreliable when data are nearly separated. A well-known solution consists of the addition of Firth' s penalty term to the log-likelihood function, and solve this penalized likelihood through logistic regression.The maximum likelihood estimates with and without Firth's penalty are compared in a large and heterogeneous population of table-tennis players. We additionally show that exact penalized maximum likelihood estimates can be reasonably approximated using a well-chosen Minorization-Maximization (MM) algorithm.

Optimal Estimation And Sampling Allocation In Survey Sampling Under A General Correlated Superpopulation Model, Ioulia Papageorgiou

Journal of Modern Applied Statistical Methods

Sampling from a finite population with correlated units is addressed. The proposed methodology applies to any type of correlation function and provides the sample allocation that ensures optimal efficiency of the population parameters estimates. The expressions of the estimate and its MSE are also provided.

An Adjusted Network Information Criterion For Model Selection In Statistical Neural Network Models, Christopher Godwin Udomboso, Godwin Nwazu Amahia, Isaac Kwame Dontwi

Journal of Modern Applied Statistical Methods

In this paper, we derived and investigated the Adjusted Network Information Criterion (ANIC) criterion, based on Kullback’s symmetric divergence, which has been designed to be an asymptotically unbiased estimator of the expected Kullback-Leibler information of a fitted model. The ANIC improves model selection in more sample sizes than does the NIC.

Monte Carlo Simulation Design For Evaluating Normal-Based Control Chart Properties, John N. Dyer

Journal of Modern Applied Statistical Methods

The advent of more complicated control charting schemes has necessitated the use of Monte Carlo simulation (MCS) methods. Unfortunately, few sources exist to study effective design and validation of MCS methods related to control charting. This paper describes the design, issues, considerations and limitations for conducting normal-based control chart MCS studies, including choice of random number generator, simulation size requirements, and accuracy/error in simulation estimation. This paper also describes two design strategies for MCS for control chart evaluations and provides the programming code. As a result, this paper hopes to establish de facto MCS schemes aimed at guiding researchers and …

Latent Variable Model For Weight Gain Prevention Data With Informative Intermittent Missingness, Li Qin, Lisa Weissfeld, Michele Levine, Marsha Marcus, Feng Dai

Journal of Modern Applied Statistical Methods

Missing data is a common problem in longitudinal studies because of the characteristics of repeated measurements. Herein is proposed a latent variable model for nonignorable intermittent missing data in which the latent variables are used as random effects in modeling and link longitudinal responses and missingness process. In this methodology, the latent variables are assumed to be normally distributed with zero-mean, and the values of variance-covariance are calculated through maximum likelihood estimations. Parameter estimates and standard errors of the proposed method are compared with the mixed model and the complete-case analysis in the simulations and the application to the weight …

E-Bayesian Estimation Of The Parameter Of The Logarithmic Series Distribution, Parviz Nasiri, Hassan Esfandyarifar

Journal of Modern Applied Statistical Methods

E-Bayesian estimation is introduced to estimate the parameter of logarithmic series distribution. In addition, E-Bayesian, Bayesian and maximum likelihood estimation with through applying mean squared error.

Jmasm41: An Alternative Method For Multiple Linear Model Regression Modeling, A Technical Combining Of Robust, Bootstrap And Fuzzy Approach (Sas), Wan Muhamad Amir W Ahmad, Mohamad Arif Awang Nawi, Nor Azlida Aleng, Mohamad Shafiq

Journal of Modern Applied Statistical Methods

Research on modeling is becoming popular nowadays, there are several of analyses used in research for modeling and one of them is known as applied multiple linear regressions (MLR). To obtain a bootstrap, robust and fuzzy multiple linear regressions, an experienced researchers should be aware the correct method of statistical analysis in order to get a better improved result. The main idea of bootstrapping is to approximate the entire sampling distribution of some estimator. To achieve this is by resampling from our original sample. In this paper, we emphasized on combining and modeling using bootstrapping, robust and fuzzy regression methodology. …

Misspecification Of Variants Of Autoregressive Garch Models And Effect On In-Sample Forecasting, Olusanya E. Olubusoye, Olaoluwa S. Yaya, Oluwadare O. Ojo

Journal of Modern Applied Statistical Methods

Generally, in empirical financial studies, the determination of the true conditional variance in GARCH modelling is largely subjective. In this paper, we investigate the consequences of choosing a wrong conditional variance specification. The methodology involves specifying a true conditional variance and then simulating data to conform to the true specification. The estimation is then carried out using the true specification and other plausible specification that are appealing to the researcher, using model and forecast evaluation criteria for assessing performance. The results show that GARCH model could serve as better alternative to other asymmetric volatility models.

Improved Ridge Estimator In Linear Regression With Multicollinearity, Heteroscedastic Errors And Outliers, Ashok Vithoba Dorugade

Journal of Modern Applied Statistical Methods

This paper introduces a new estimator, of ridge parameter k for ridge regression and then evaluated by Monte Carlo simulation. We examine the performance of the proposed estimators compared with other well-known estimators for the model with heteroscedastics and/or correlated errors, outlier observations, non-normal errors and suffer from the problem of multicollinearity. It is shown that proposed estimators have a smaller MSE than the ordinary least squared estimator (LS), Hoerl and Kennard (1970) estimator (RR), jackknifed modified ridge (JMR) estimator, and Jackknifed Ridge M‑estimator (JRM).

Multicollinearity And A Ridge Parameter Estimation Approach, Ghadban Khalaf, Mohamed Iguernane

Journal of Modern Applied Statistical Methods

One of the main goals of the multiple linear regression model, Y = Xβ + u, is to assess the importance of independent variables in determining their predictive ability. However, in practical applications, inference about the coefficients of regression can be difficult because the independent variables are correlated and multicollinearity causes instability in the coefficients. A new estimator of ridge regression parameter is proposed and evaluated by simulation techniques in terms of mean squares error (MSE). Results of the simulation study indicate that the suggested estimator dominates ordinary least squares (OLS) estimator and other ridge estimators with respect to …

Estimation Of Parameters Of Misclassified Size Biased Borel Distribution, Bhaktida S. Trivedi, M. N. Patel

Journal of Modern Applied Statistical Methods

A misclassified size-biased Borel Distribution (MSBBD), where some of the observations corresponding to x = c + 1 are wrongly reported as x = c with probability α, is defined. Various estimation methods like the method of maximum likelihood (ML), method of moments, and the Bayes estimation for the parameters of the MSBB distribution are used. The performance of the estimators are studied using simulated bias and simulated risk. Simulation studies are carried out for different values of the parameters and sample size.

Developing Bayesian-Based Confidence Bounds For Non-Identically Distributed Observations Using The Lyapunov Condition, Garry M. Jacyna, Scott L. Rosen

Journal of Modern Applied Statistical Methods

The purpose of this paper is to establish a direct method for assessing the confidence in the detection and identification probabilities for segmented observations that are not identically distributed across assigned segments within a region. This paper arrives at easily computable confidence intervals by showing through mathematical analysis that:

I. The probability of successful detection within each test segment can be characterized by a Beta distribution;
II. The distribution of a weighted sum of independent but non-identically distributed sample means is asymptotically Normally distributed by the Lyapunov variant of the Central Limit Theorem, i.e., the approximation improves as the number …

Jmasm40: Monte Carlo Simulations For Structural Equation Modelling (Revolution R), Sarah A. Rose, Barry Markman

Journal of Modern Applied Statistical Methods

Revolution R code is presented to setup Structural Equation Model (SEM) for a Monte Carlo study. The example is a comparison of different fit indices.

Reflections Concerning Recent Ban On Nhst And Confidence Intervals, Grayson L. Baird, Sunny R. Duerr

Journal of Modern Applied Statistical Methods

This letter addresses some of the immediate consequences of Basic and Applied Social Psychology’s (BASP) ban on null hypothesis significance testing (NHST) and confidence intervals. The letter concludes with three suggestions to improve research in general.

A New Test For Correlation On Bivariate Nonnormal Distributions, Ping Wang, Ping Sa

Journal of Modern Applied Statistical Methods

A new method to conduct a right-tailed test for the correlation on bivariate non-normal distribution is proposed. The comparative simulation study shows that the new test controls the type I error rates well for all the distributions considered. An investigation of the power performance is also provided.

Jmasm42: An Alternative Algorithm And Programming Implementation For Least Absolute Deviation Estimator Of The Linear Regression Models (R), Suraju Olaniyi Ogundele, J. I. Mbegbu, C. R. Nwosu

Journal of Modern Applied Statistical Methods

We propose a least absolute deviation estimation method that produced a least absolute deviation estimator of parameter of the linear regression model. The method is as accurate as existing method.

Application Of Esscher Transformed Laplace Distribution In Microarray Gene Expression Data, Shanmugasundaram Devika, Sebastian George, Lakshmanan Jeyaseelan

Journal of Modern Applied Statistical Methods

Microarrays allow the study of the expression profile of hundreds to thousands of genes simultaneously. These expressions could be from treated samples and the healthy controls. The Esscher transformed Laplace distribution is used to fit microarray expression data as compared to Normal and Laplace distributions. The Maximum Likelihood Estimation procedure is used to estimate the parameters of the distribution. R codes are developed to implement the estimation procedure. A simulation study is carried out to test the performance of the algorithm. AIC and BIC criterion are used to compare the distributions. It is shown that the fit of the Esscher …

The Goldilocks Dilemma: Impacts Of Multicollinearity -- A Comparison Of Simple Linear Regression, Multiple Regression, And Ordered Variable Regression Models, Grayson L. Baird, Stephen L. Bieber

Journal of Modern Applied Statistical Methods

A common consideration concerning the application of multiple linear regression is the lack of independence among predictors (multicollinearity). The main purpose of this article is to introduce an alternative method of regression originally outlined by Woolf (1951), which completely eliminates the relatedness between the predictors in a multiple predictor setting.

Solution To The Multicollinearity Problem By Adding Some Constant To The Diagonal, Hanan Duzan, Nurul Sima Binti Mohamaed Shariff

Journal of Modern Applied Statistical Methods

Ridge regression is an alternative to ordinary least-squares (OLS) regression. It is believed to be superior to least-squares regression in the presence of multicollinearity. The robustness of this method is investigated and comparison is made with the least squares method through simulation studies. Our results show that the system stabilizes in a region of k, where k is a positive quantity less than one and whose values depend on the degree of correlation between the independent variables. The results also illustrate that k is a linear function of the correlation between the independent variables.

Symmetric Variants Of Logistic Smooth Transition Autoregressive Models: Monte Carlo Evidences, Olaoluwa S. Yaya, Olanrewaju I. Shittu

Journal of Modern Applied Statistical Methods

The Smooth Transition Autoregressive (STAR) models are becoming popular in modeling economic and financial time series. The asymmetric type of the model is the Logistic STAR (LSTAR) model, which is limited in its applications as a result of its asymmetric property, which makes it suitable for modelling specific macroeconomic time series. This study was designed to develop the Absolute Error LSTAR (AELSTAR) and Quadratic LSTAR (QLSTAR) models for improving symmetry and performance in terms of model fitness. Modified Teräsvirta’s Procedure (TP) and Escribano and Jordá's Procedure (EJP) were used to test for nonlinearity in the series. The performance of the …

Factorial Invariance Testing Under Different Levels Of Partial Loading Invariance Within A Multiple Group Confirmatory Factor Analysis Model, Brian F. French, Holmes Finch

Journal of Modern Applied Statistical Methods

Scalar invariance in factor models is important for comparing latent means. Little work has focused on invariance testing for other model parameters under various conditions. This simulation study assesses how partial factorial invariance influences invariance testing for model parameters. Type I error inflation and parameter bias were observed.

Jmasm36: Nine Pseudo R^2 Indices For Binary Logistic Regression Models (Spss), David A. Walker, Thomas J. Smith

Journal of Modern Applied Statistical Methods

This syntax program is an applied complement to Veall and Zimmermann (1994), Menard (2000), and Smith and McKenna (2013) and produces nine pseudo R² indices, not readily accessible in statistical software such as SPSS, which are used to describe the results from binary logistic regression analyses.

A Spatial Analytical Framework For Examining Road Traffic Crashes, Grace O. Korter

Journal of Modern Applied Statistical Methods

A number of different modeling techniques have been used to examine road traffic crashes for analytic and predictive purposes. Map-based spatial analysis is introduced. Applications are given which show the power in a combination of existing exploratory and statistical methods.

Jmasm38: Confidence Intervals For Kendall's Tau With Small Samples (Spss), David A. Walker

Journal of Modern Applied Statistical Methods

A syntax program, not readily expedient in statistical software such as SPSS, is provided for an application of confidence interval estimates with Kendall’s tau-b for small samples.

An Evaluation Of Pareto, Lognormal And Pps Distributions: The Size Distribution Of Cities In Kerala, India, Christopher A. Vallabados, Subbarayan A. Arumugam

Journal of Modern Applied Statistical Methods

The Pareto-Positive Stable (PPS) distribution is introduced as a new model for describing city size data of a region in a country. The PPS distribution provides a flexible model for fitting the entire range of a set of city size data and the classical Pareto and Zipf distributions are included as a particular case.