Statistics and Probability Commons^™

On The Appropriate Transformation Technique And Model Selection In Forecasting Economic Time Series: An Application To Botswana Gdp Data, D. K. Shangodoyin, K. Setlhare, K. K. Moseki, K. Sediakgotla

Journal of Modern Applied Statistical Methods

Selected data transformation techniques in time series modeling are evaluated using real-life data on Botswana Gross Domestic Product (GDP). The transformation techniques considered were modified, although reasonable estimates of the original with no significant difference at α = 0.05 level were obtained: minimizing square of first difference (MFD) and minimizing square of second difference (MSD) provided the best transformation for GDP, whereas the Goldstein and Khan (GKM) method had a deficiency of losing data points. The Box-Jenkins procedure was adapted to fit suitable ARIMA (p, d, q) models to both the original and transformed series, with AIC and SIC as …

A New Biased Estimator Derived From Principal Component Regression Estimator, Set Foong Ng, Heng Chin Low, Soon Hoe Quah

Journal of Modern Applied Statistical Methods

A new biased estimator obtained by combining the Principal Component Regression Estimator and the special case of Liu-type estimator is proposed. The properties of the new estimator are derived and comparisons between the new estimator and other estimators in terms of mean squared error are presented.

Optimal Meter Placement By Reconciliation Conventional Measurements And Phasor Measurement Units (Pmus), Reza Kaihani, Ali Reza Seifi

Journal of Modern Applied Statistical Methods

The success of state estimation depends on the number, type and location of the established meters and RTUs on the system. A new method by incorporating conventional measurements and New Technology of Phasor Measurement Units (PMU) is proposed. Conventional meters (power injection and power flow measurements) are allocated in order to reduce the number of meters, RTUs, critical measurements, critical sets and leverage points, and also to improve the numerical stability of equations; a genetic algorithm is used for optimization. A second step involves adding PMUs in areas in which it is expected that the accuracy of state estimation will …

Fisher Was Right, Ronald C. Serlin

Journal of Modern Applied Statistical Methods

Invited address presented to the Educational Statistician’s Special Interest Group at the annual meeting of the American Educational Research Association, Denver, May 1, 2010.

Inferences About The Population Mean: Empirical Likelihood Versus Bootstrap-T, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

The problem of making inferences about the population mean, μ, is considered. Known theoretical results suggest that a Bartlett corrected empirical likelihood method is preferable to two basic bootstrap techniques: a symmetric two-sided bootstrap-t and an equal-tailed bootstrap-t. However, simulations in this study indicate that, when the sample size is small, these two bootstrap methods are generally better in terms of Type I errors and probability coverage. As the sample size increases, situations are found where the Bartlett corrected empirical likelihood method performs better than the equal-tailed bootstrap-t, but the symmetric bootstrap-t gives the best results. None of the four …

The Influence Of Data Generation On Simulation Study Results: Tests Of Mean Differences, Tim Moses, Alan Klockars

Journal of Modern Applied Statistical Methods

Type I error and power of the standard independent samples t-test were compared with the trimmed and Winsorized t-test with respect to continuous distributions and various discrete distributions known to occur in applied data. The continuous and discrete distributions were generated with similar levels of skew and kurtosis but the discrete distributions had a variety of structural features not reflected in the continuous distributions. The results showed that the Type I error rates of the t-tests were not seriously affected, but the power rate of the trimmed and Winsorized t-test varied greatly across the considered distributions.

The Small-Sample Efficiency Of Some Recently Proposed Multivariate Measures Of Location, Marie Ng, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

Numerous multivariate robust measures of location have been proposed and many have been found to be unsatisfactory in terms of their small-sample efficiency. Several new measures of location have recently been derived, however, nothing is known about their small-sample efficiency or how they compare to the sample mean under normality. This research compared the efficiency for p = 2, 5, and 8 with sample sizes n = 20 and 50 for p-variate data. Although previous studies indicate that so-called skipped estimators are efficient, this study found that variations of this approach can perform poorly when n is small and p …

Assessing Classification Bias In Latent Class Analysis: Comparing Resubstitution And Leave-One-Out Methods, Marc H. Kroopnick, Jinsong Chen, Jaehwa Choi, C. Mitchell Dayton

Journal of Modern Applied Statistical Methods

This Monte Carlo simulation study assessed the degree of classification success associated with resubstitution methods in latent class analysis (LCA) and compared those results to those of the leaveone- out (L-O-O) method for computing classification success. Specifically, this study considered a latent class model with two classes, dichotomous manifest variables, restricted conditional probabilities for each latent class and relatively small sample sizes. The performance of resubstitution and L-O-O methods on the lambda classification index was assessed by examining the degree of bias.

Nonlinear Parameterization In Bi-Criteria Sample Balancing, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Sample balancing is widely used in applied research to adjust a sample data to achieve better correspondence to Census statistics. The classic Deming-Stephan iterative proportional approach finds the weights of observations by fitting the cross-tables of sample counts to known margins. This work considers a bi-criteria objective for finding weights with maximum possible effective base size. This approach is presented as a ridge regression with the exponential nonlinear parameterization that produces nonnegative weights for sample balancing.

Jmasm30 Pi-Lca: A Sas Program Computing The Two-Point Mixture Index Of Fit For Two-Class Lca Models With Dichotomous Variables (Sas), Dongquan Zhang, C. Mitchell Dayton

Journal of Modern Applied Statistical Methods

The two-point mixture index of fit enjoys some desirable features in model fit assessment and model selection, however, a need exists for efficient computational strategies. Applying an NLP algorithm, a program using the SAS matrix language is presented to estimate the two-point index of fit for two-class LCA models with dichotomous response variables. The program offers a tool to compute π ∗ for twoclass models and it also provides an alternative program for conducting latent class analysis with SAS. This study builds a foundation for further research on computational approaches for M-class models.

Another Look At Resampling: Replenishing Small Samples With Virtual Data Through S-Smart, Haiyan Bai, Wei Pan, Leigh Lihshing Wang, Phillip Neal Ritchey

Journal of Modern Applied Statistical Methods

A new resampling method is introduced to generate virtual data through a smoothing technique for replenishing small samples. The replenished analyzable sample retains the statistical properties of the original small sample, has small standard errors and possesses adequate statistical power.

Estimations On The Generalized Exponential Distribution Using Grouped Data, Hassan Pazira, Parviz Nasiri

Journal of Modern Applied Statistical Methods

Classical and Bayesian estimators are obtained for the shape parameter of the Generalized-Exponential distribution under grouped data. In Bayesian estimation, three types of loss functions are considered: the Squared Error loss function which is classified as a symmetric function, the LINEX and Precautionary loss functions which are asymmetric. These estimators are compared with the corresponding estimators derived from un-grouped data empirically using Monte-Carlo simulation.

Symmetry Plus Quasi Uniform Association Model And Its Orthogonal Decomposition For Square Contingency Tables, Kouji Yamamoto, Sadao Tomizawa

Journal of Modern Applied Statistical Methods

A model is proposed having the structure of both symmetry and quasi-uniform association (SQU model) and provides a decomposition of the SQU model. It is also shown with examples that the test statistic for goodness-of-fit of the SQU model is asymptotically equivalent to the sum of those for the decomposed models.

Applying Multiple Imputation With Geostatistical Models To Account For Item Nonresponse In Environmental Data, Breda Munoz, Virginia M. Lesser, Ruben A. Smith

Journal of Modern Applied Statistical Methods

Methods proposed to solve the missing data problem in estimation procedures should consider the type of missing data, the missing data mechanism, the sampling design and the availability of auxiliary variables correlated with the process of interest. This article explores the use of geostatistical models with multiple imputation to deal with missing data in environmental surveys. The method is applied to the analysis of data generated from a probability survey to estimate Coho salmon abundance in streams located in western Oregon watersheds.

Beyond Alpha: Lower Bounds For The Reliability Of Tests, Nol Bendermacher

Journal of Modern Applied Statistical Methods

The most common lower bound to the reliability of a test is Cronbach’s alpha. However, several lower bounds exist that are definitely better, that is, higher than alpha. An overview is given as well as an algorithm to find the best: the greatest lower bound.

Shrinkage Estimation In The Inverse Rayleigh Distribution, Gyan Prakash

Journal of Modern Applied Statistical Methods

The properties of the shrinkage test–estimators of the parameter were studied for an inverse Rayleigh model under the asymmetric loss function. Both the single and double–stage shrinkage test–estimators are considered.

Combining Independent Tests Of Conditional Shifted Exponential Distribution, Abedel-Qader S. Al-Masri

Journal of Modern Applied Statistical Methods

The problem of combining n independent tests as n→∞ for testing that variables are uniformly distributed over the interval (0, 1) compared to their having a conditional shifted exponential distribution with probability density function f (xθ ) = e^{−(x−γθ)} , x ≥γθ , θ ∈[a,∞), a ≥ 0 was studied. This was examined for the case where θ₁, θ₂, … are distributed according to the distribution function (DF) F and when the DF is Gamma (1, 2). Six omnibus methods were compared via the Bahadur efficiency. It is shown that, as γ → 0 and …

A Comparative Study For Bandwidth Selection In Kernel Density Estimation, Omar M. Eidous, Mohammad Abd Alrahem Shafeq Marie, Mohammed H. Baker Al-Haj Ebrahem

Journal of Modern Applied Statistical Methods

Nonparametric kernel density estimation method does not make any assumptions regarding the functional form of curves of interest; hence it allows flexible modeling of data. A crucial problem in kernel density estimation method is how to determine the bandwidth (smoothing) parameter. This article examines the most important bandwidth selection methods, in particular, least squares cross-validation, biased crossvalidation, direct plug-in, solve-the-equation rules and contrast methods. Methods are described and expressions are presented. The main practical contribution is a comparative simulation study that aims to isolate the most promising methods. The performance of each method is evaluated on the basis of the …

Type Ii Robustness Of The Null Hypothesis Rho = 0 For Non-Normal Distributions, Stephanie Wren

Wayne State University Dissertations

Is the t test statistic for the Pearson Product Moment Correlation Coefficient robust to errors of the second kind? This investigation indirectly measured the effects of power through a type 2 error rate robustness study. The results were revealing.

Identification Of Neuroblastoma And Its Prognostic Markers Using Raman Spectroscopy, Rachel Kast

Wayne State University Dissertations

Introduction: Neuroblastoma is the most common cancer of infancy. It is one of several peripheral nervous system tumors, including ganglioneuroma, peripheral nerve sheath tumor, and pheochromocytoma. It is commonly situated on the adrenal gland. It displays similar histology to other small round blue cell tumors, including non-Hodgkin lymphoma, rhabdomyosarcoma, and Ewing sarcoma. One method of judging neuroblastoma aggressiveness uses tumor histology factors, including mitosis-karyorrhexis index, Schwannian stromal development, degree of differentiation, and patient age. Tumor aggressiveness can also be judged based on the amplification of certain genes, including MYCN. Raman spectroscopy is a physics-based method which identifies the biochemical …

Critical Values For The Two Independent Samples Winsorized T Test, Piper Alycee Farrell-Singleton

Wayne State University Dissertations

ABSTRACT

CRITICAL VALUES FOR THE TWO INDEPENDENT SAMPLES WINSORIZED T TEST

by

PIPER A. FARRELL-SINGLETON

AUGUST 2010

Advisor: Dr. Shlomo Sawilowsky

Major: (Education, Evaluation and Research)

Degree: Doctor of Philosophy

Through Monte Carlo Simulation, this study explores the approximate behavior of the two sample winsorized t test. Samples are drawn from the normal population and symetrically winsorized up to 20%. The two independent samples winsorized t test is then calculated on each sample using Monte Carlo methods using 1,000,000 iterations. The t values are then sorted from low to high and the critical values for both one and two tailed …

Application Of The Truncated Skew Laplace Probability Distribution In Maintenance System, Gokarna R. Aryal, Chris P. Tsokos

Journal of Modern Applied Statistical Methods

A random variable X is said to have the skew-Laplace probability distribution if its pdf is given by f(x) = 2g(x)G(λx), where g (.) and G (.), respectively, denote the pdf and the cdf of the Laplace distribution. When the skew Laplace distribution is truncated on the left at 0 it is called it the truncated skew Laplace (TSL) distribution. This article provides a comparison of TSL distribution with twoparameter gamma model and the hypoexponential model, and an application of the subject model in maintenance system is studied.

Examples Of Computing Power For Zero-Inflated And Overdispersed Count Data, Suzanne R. Doyle

Journal of Modern Applied Statistical Methods

Examples of zero-inflated Poisson and negative binomial regression models were used to demonstrate conditional power estimation, utilizing the method of an expanded data set derived from probability weights based on assumed regression parameter values. SAS code is provided to calculate power for models with a binary or continuous covariate associated with zero-inflation.

An Inductive Approach To Calculate The Mle For The Double Exponential Distribution, W. J. Hurley

Journal of Modern Applied Statistical Methods

Norton (1984) presented a calculation of the MLE for the parameter of the double exponential distribution based on the calculus. An inductive approach is presented here.

New Effect Size Rules Of Thumb, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

Recommendations to expand Cohen’s (1988) rules of thumb for interpreting effect sizes are given to include very small, very large, and huge effect sizes. The reasons for the expansion, and implications for designing Monte Carlo studies, are discussed.

Generating And Comparing Aggregate Variables For Use Across Datasets In Multilevel Analysis, James Chowhan, Laura Duncan

Journal of Modern Applied Statistical Methods

This article examines the creation of contextual aggregate variables from one dataset for use with another dataset in multilevel analysis. The process of generating aggregate variables and methods of assessing the validity of the constructed aggregates are presented, together with the difficulties that this approach presents.

Detecting Lag-One Autocorrelation In Interrupted Time Series Experiments With Small Datasets, Clare Riviello, S. Natasha Beretvas

Journal of Modern Applied Statistical Methods

The power and type I error rates of eight indices for lag-one autocorrelation detection were assessed for interrupted time series experiments (ITSEs) with small numbers of data points. Performance of Huitema and McKean’s (2000) z_HM statistic was modified and compared with the z_HM, five information criteria and the Durbin-Watson statistic.

Relationship Between Internal Consistency And Goodness Of Fit Maximum Likelihood Factor Analysis With Varimax Rotation, Gibbs Y. Kanyongo, James B. Schreiber

Journal of Modern Applied Statistical Methods

This study investigates how reliability (internal consistency) affects model-fitting in maximum likelihood exploratory factor analysis (EFA). This was accomplished through an examination of goodness of fit indices between the population and the sample matrices. Monte Carlo simulations were performed to create pseudo-populations with known parameters. Results indicated that the higher the internal consistency the worse the fit. It is postulated that the observations are similar to those from structural equation modeling where a good fit with low correlations can be observed and also the reverse with higher item correlations.

Estimating Model Complexity Of Feed-Forward Neural Networks, Douglas Landsittel

Journal of Modern Applied Statistical Methods

In a previous simulation study, the complexity of neural networks for limited cases of binary and normally-distributed variables based the null distribution of the likelihood ratio statistic and the corresponding chi-square distribution was characterized. This study expands on those results and presents a more general formulation for calculating degrees of freedom.

Level Robust Methods Based On The Least Squares Regression Estimator, Marie Ng, Rand R. Wilcox

Journal of Modern Applied Statistical Methods

Heteroscedastic consistent covariance matrix (HCCM) estimators provide ways for testing hypotheses about regression coefficients under heteroscedasticity. Recent studies have found that methods combining the HCCM-based test statistic with the wild bootstrap consistently perform better than non-bootstrap HCCM-based methods (Davidson & Flachaire, 2008; Flachaire, 2005; Godfrey, 2006). This finding is more closely examined by considering a broader range of situations which were not included in any of the previous studies. In addition, the latest version of HCCM, HC5 (Cribari-Neto, et al., 2007), is evaluated.