Statistical Theory Commons^™

Wald Confidence Intervals For A Single Poisson Parameter And Binomial Misclassification Parameter When The Data Is Subject To Misclassification, Nishantha Janith Chandrasena Poddiwala Hewage

Electronic Theses and Dissertations

This thesis is based on a Poisson model that uses both error-free data and error-prone data subject to misclassification in the form of false-negative and false-positive counts. We present maximum likelihood estimators (MLEs), Fisher's Information, and Wald statistics for Poisson rate parameter and the two misclassification parameters. Next, we invert the Wald statistics to get asymptotic confidence intervals for Poisson rate parameter and false-negative rate parameter. The coverage and width properties for various sample size and parameter configurations are studied via a simulation study. Finally, we apply the MLEs and confidence intervals to one real data set and another realistic …

A Distance Based Method For Solving Multi-Objective Optimization Problems, Murshid Kamal, Syed Aqib Jalil, Syed Mohd Muneeb, Irfan Ali

Journal of Modern Applied Statistical Methods

A new model for the weighted method of goal programming is proposed based on minimizing the distances between ideal objectives to feasible objective space. It provides the best compromised solution for Multi Objective Linear Programming Problems (MOLPP). The proposed model tackles MOLPP by solving a series of single objective sub-problems, where the objectives are transformed into constraints. The compromise solution so obtained may be improved by defining priorities in terms of the weight. A criterion is also proposed for deciding the best compromise solution. Applications of the algorithm are discussed for transportation and assignment problems involving multiple and conflicting objectives. …

Estimation Of Finite Population Mean By Using Minimum And Maximum Values In Stratified Random Sampling, Umer Daraz, Javid Shabbir, Hina Khan

Journal of Modern Applied Statistical Methods

In this paper we have suggested an improved class of ratio type estimators in estimating the finite population mean when information on minimum and maximum values of the auxiliary variable is known. The properties of the suggested class of estimators in terms of bias and mean square error are obtained up to first order of approximation. Two data sets are used for efficiency comparisons.

A Bayesian Beta-Mixture Model For Nonparametric Irt (Bbm-Irt), Ethan A. Arenson, George Karabatsos

Journal of Modern Applied Statistical Methods

Item response models typically assume that the item characteristic (step) curves follow a logistic or normal cumulative distribution function, which are strictly monotone functions of person test ability. Such assumptions can be overly-restrictive for real item response data. A simple and more flexible Bayesian nonparametric IRT model for dichotomous items is introduced, which constructs monotone item characteristic (step) curves by a finite mixture of beta distributions, which can support the entire space of monotone curves to any desired degree of accuracy. An adaptive random-walk Metropolis-Hastings algorithm is proposed to estimate the posterior distribution of the model parameters. The Bayesian IRT …

Robust Estimation And Inference On Current Status Data With Applications To Phase Iv Cancer Trial, Deo Kumar Srivastava, Liang Zhu, Melissa M. Hudson, Jianmin Pan, Shesh N. Rai

Journal of Modern Applied Statistical Methods

The use of piecewise exponential distributions was proposed by Rai et al. (2013) for analyzing cardiotoxicity data. Some parametric models are proposed, but the focus is on the Weibull distribution, which overcomes the limitation of piecewise exponential.

Robust Heteroscedasticity Consistent Covariance Matrix Estimator Based On Robust Mahalanobis Distance And Diagnostic Robust Generalized Potential Weighting Methods In Linear Regression, M. Habshah, Muhammad Sani, Jayanthi Arasan

Journal of Modern Applied Statistical Methods

The violation of the assumption of homoscedasticity and the presence of high leverage points (HLPs) are common in the use of regression models. The weighted least squares can provide the solution to heteroscedastic regression model if the heteroscedastic error structures are known. Based on Furno (1996), two robust weighting methods are proposed based on HLP detection measures (robust Mahalanobis distance based on minimum volume ellipsoid and diagnostic robust generalized potential based on index set equality (DRGP(ISE)) on robust heteroscedasticity consistent covariance matrix estimators. Results obtained from a simulation study and real data sets indicated the DRGP(ISE) method is superior.

Internal Consistency Reliability In Measurement: Aggregate And Multilevel Approaches, Georgios Sideridis, Abdullah Saddaawi, Khaleel Al-Harbi

Journal of Modern Applied Statistical Methods

The purpose of the present paper was to evaluate the internal consistency reliability of the General Teacher Test assuming clustered and non-clustered data using commercial software (Mplus). Participants were 2,000 testees who were selected using random sampling from a larger pool of examinees (more than 65k). The measure involved four factors, namely: (a) planning for learning, (b) promoting learning, (c) supporting learning, and (d) professional responsibilities and was hypothesized to comprise a unidimensional instrument assessing generalized skills and competencies. Intra-class correlation coefficients and variance ratio statistics suggested the need to incorporate a clustering variable (i.e., university) when evaluating the factor …

Fitting The Rasch Model Under The Logistic Regression Framework To Reduce Estimation Bias, Tianshu Pan

Journal of Modern Applied Statistical Methods

This article showed how and why the Rasch model can be fitted under the logistic regression framework. Then a penalized maximum likelihood (Firth 1993) for logistic regression models can also be used to reduce ML biases when fitting the Rasch model. These conclusions are supported by a simulation study.

Regressions Regularized By Correlations, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

The regularization of multiple regression by proportionality to correlations of predictors with dependent variable is applied to the least squares objective and normal equations to relax the exact equalities and to get a robust solution. This technique produces models not prone to multicollinearity and is very useful in practical applications.

An Explanatory Study On The Non-Parametric Multivariate T2 Control Chart, Abdolrasoul Mostajeran, Nasrolah Iranpanah, Rassoul Noorossana

Journal of Modern Applied Statistical Methods

Most control charts require the assumption of normal distribution for observations. When distribution is not normal, one can use non-parametric control charts such as sign control chart. A deficiency of such control charts could be the loss of information due to replacing an observation with its sign or rank. Furthermore, because the chart statistics of T² are correlated, the T² chart is not a desire performance. Non-parametric bootstrap algorithm could help to calculate control chart parameters using the original observations while no assumption regarding the distribution is needed. In this paper, first, a bootstrap multivariate control chart is …

Optimum Stratification In Bivariate Auxiliary Variables Under Neyman Allocation, Faizan Danish, S.E.H. Rizvi

Journal of Modern Applied Statistical Methods

In several situations complete data set of the study variable is unknown that becomes a stumbling block in various stratification techniques in order to obtain stratification points on two way stratification method. In this paper a technique has been proposed under Neyman allocation when the stratification is done oj the two auxiliary variable having one estimation variable under consideration. Due to complexities created by minimal equations approximate optimum strata boundaries has been obtained. Empirical study has been done to illustrate the proposed method when the auxiliary variables have standard Cauchy and power distributions.

Estimation Of Zero-Inflated Population Mean: A Bootstrapping Approach, Khyam Paneru, R. Noah Padgett, Hanfeng Chen

Journal of Modern Applied Statistical Methods

A mixture model was adopted from the maximum pseudo-likelihood approach under complex sampling designs to estimate the mean of zero-inflated population. To overcome the complexity and assumptions of asymptotic distribution, the maximum pseudo-likelihood function was used, but a bootstrapping procedure was proposed as an alternative. Bootstrap confidence intervals consistently capture the true means of zero-inflated populations of the simulation studies.

Moment Generating Functions Of Complementary Exponential-Geometric Distribution Based On K-Th Lower Record Values, Devendra Kumar, Sanku Dey, Mansoor Rashid Malik, Fahad M. Al-Aboud

Journal of Modern Applied Statistical Methods

The complementary exponential-geometric (CEG) distribution is a useful model for analyzing lifetime data. For this distribution, some recurrence relations satisfied by marginal and joint moment generating functions of k-th lower record values were established. They enable the computation of the means, variances, and covariances of k-th lower record values for all sample sizes in a simple and efficient recursive manner. Means, variances, and covariances of lower record values were tabulated from samples of sizes up to 10 for various values of the parameters.

Optimal Model Selection For Truncated Data Among Non-Nested Competitive Models, Parisa Torkaman

Journal of Modern Applied Statistical Methods

Selecting a model for incomplete data is an important issue. Truncated data is an example of incomplete data, which sometimes occurs due to inherent limitations. The maximum likelihood estimator features and its asymptotic distribution are studied, and a test statistic among non-nested competitive model of incomplete data is presented, which can select an appropriate model close to the true model. This close-to-true model under the null hypothesis of the equivalency of two competitive models against alternative hypothesis is selected.

Letter To The Editor: Regarding A Possible Non-Null Interpretation Of The Michelson-Morley Experiment, Maurizio Consoli

Journal of Modern Applied Statistical Methods

The author writes in response to Sawilowsky in JMASM 2(2) and 4(1).

The Transmuted Exponentiated Additive Weibull Distribution: Properties And Applications, Zohdy M. Nofal, Ahmed Z. Afify, Haitham M. Yousof, Daniele Cristina Tita Granzotto, Francisco Louzada

Journal of Modern Applied Statistical Methods

A new generalization of the transmuted additive Weibull distribution is proposed by using the quadratic rank transmutation map, the so-called transmuted exponentiated additive Weibull distribution. It retains the characteristics of a good model. It is more flexible, being able to analyze more complex data; it includes twenty-seven sub-models as special cases and it is interpretable. Several mathematical properties of the new distribution as closed forms for ordinary and incomplete moments, quantiles, and moment generating function are presented, as well as the MLEs. The usefulness of the model is illustrated by using two real data sets.

Modeling Insurance Claims Using Flexible Skewed And Mixture Probability Distributions, Aaron J. Leinwander, Mohammad A. Aziz

Journal of Modern Applied Statistical Methods

The normal distribution comes as a first choice when fitting real data, but it may not be suitable if the assumed distribution deviates from normality. Flexible skewed distributions are capable of including skewness and taking into account multimodality. They may be applied to find appropriate distributions for describing the claim amounts in insurance. The objective is to model insurance claims using a set of flexible skewed and mixture probability distributions, and to test how well they fit the claims. Results indicate the skew-t distribution and alpha-skew Laplace distribution are able to describe unimodal claims accurately, whereas scale mixture of …

Single Missing Data Imputation In Pls-Based Structural Equation Modeling, Ned Kock

Journal of Modern Applied Statistical Methods

Missing data, a source of bias in structural equation modeling (SEM) employing the partial least squares method (PLS), are commonly handled with deletion methods such as listwise and pairwise deletion. Missing data imputation methods do not resort to deletion. Five single missing data imputation methods are considered employing the PLS Mode A algorithm of which two hierarchical methods are new. The results of a Monte Carlo experiment suggest that Multiple Regression Imputation yielded the least biased mean path coefficient estimates, followed by Arithmetic Mean Imputation. With respect to mean loading estimates, Arithmetic Mean Imputation yielded the least biased results, followed …

A New Lifetime Distribution For Series System: Model, Properties And Application, Adil Rashid, Zahooor Ahmad, T R. Jan

Journal of Modern Applied Statistical Methods

A new lifetime distribution for modeling system lifetime in series setting is proposed that embodies most of the compound lifetime distribution. The reliability analysis of parent and of sub-models has also been discussed. Various mathematical properties that include moment generating function, moments, and order statistics have been obtained. The newly-proposed distribution has a flexible density function; more importantly its hazard rate function can take up different shapes such as bathtub, upside down bathtub, increasing, and decreasing shapes. The unknown parameters of the proposed generalized family have been estimated through MLE technique. The strength and usefulness of the proposed family was …

An Inferential Method For Determining Which Of Two Independent Variables Is Most Important When There Is Curvature, Rand Wilcox

Journal of Modern Applied Statistical Methods

Consider three random variables Y, X₁ and X₂, where the typical value of Y, given X₁ and X₂, is given by some unknown function m(X₁, X₂). A goal is to determine which of the two independent variables is most important when both variables are included in the model. Let τ₁ denote the strength of the association associated with Y and X₁, when X₂ is included in the model, and let τ₂ be defined in an analogous manner. If it is assumed …

Sample Size For Non-Inferiority Tests For One Proportion: A Simulation Study, Özlem Güllü, Mustafa Agah Tekindal

Journal of Modern Applied Statistical Methods

The objective of non-inferiority trials is to demonstrate the efficiency of a novel treatment whether it is acceptably less or more efficient than a control or active (existing) treatment. They are employed in situations where, when compared to the active treatment, the novel treatment is to be advantageous with higher rates of reliability, compatibility, cost-efficiency, etc. Odds ratio is the most significant measure used in investigating the size of efficiency of treatments relative to one another. The purpose of the study is to calculate and evaluate the sample size under different scenarios based on three different test statistics in non-inferiority …

Handling Missing Data In Single-Case Studies, Chao-Ying Joanne Peng, Li-Ting Chen

Journal of Modern Applied Statistical Methods

Multiple imputation is illustrated for dealing with missing data in a published SCED study. Results were compared to those obtained from available data. Merits and issues of implementation are discussed. Recommendations are offered on primal/advanced readings, statistical software, and future research.

Evaluation Of Using The Bootstrap Procedure To Estimate The Population Variance, Nghia Trong Nguyen

Electronic Theses and Dissertations

The bootstrap procedure is widely used in nonparametric statistics to generate an empirical sampling distribution from a given sample data set for a statistic of interest. Generally, the results are good for location parameters such as population mean, median, and even for estimating a population correlation. However, the results for a population variance, which is a spread parameter, are not as good due to the resampling nature of the bootstrap method. Bootstrap samples are constructed using sampling with replacement; consequently, groups of observations with zero variance manifest in these samples. As a result, a bootstrap variance estimator will carry a …

Evaluating The Efficacy Of Conditional Analysis Of Variance Under Heterogeneity And Non-Normality, Yan Wang, Thanh Pham, Diep Nguyen, Eun Sook Kim, Yi-Hsin Chen, Jeffrey Kromrey, Zhiyao Yi, Yue Yin

Journal of Modern Applied Statistical Methods

A simulation study was conducted to examine the efficacy of conditional analysis of variance (ANOVA) methods where the initial homogeneity of variance screening leads to the choice between the ANOVA F test and robust ANOVA methods. Type I error control and statistical power were investigated under various conditions.

The Family Of Conditional Penalized Methods With Their Application In Sufficient Variable Selection, Jin Xie

Theses and Dissertations--Statistics

When scientists know in advance that some features (variables) are important in modeling a data, then these important features should be kept in the model. How can we utilize this prior information to effectively find other important features? This dissertation is to provide a solution, using such prior information. We propose the Conditional Adaptive Lasso (CAL) estimates to exploit this knowledge. By choosing a meaningful conditioning set, namely the prior information, CAL shows better performance in both variable selection and model estimation. We also propose Sufficient Conditional Adaptive Lasso Variable Screening (SCAL-VS) and Conditioning Set Sufficient Conditional Adaptive Lasso Variable …

Effect Of Neuromodulation Of Short-Term Plasticity On Information Processing In Hippocampal Interneuron Synapses, Elham Bayat Mokhtari

Graduate Student Theses, Dissertations, & Professional Papers

Neurons convey information about the complex dynamic environment in the form of signals. Computational neuroscience provides a theoretical foundation toward enhancing our understanding of nervous system. The aim of this dissertation is to present techniques to study the brain and how it processes information in particular neurons in hippocampus.

We begin with a brief review of the history of neuroscience and biological background of basic neurons. To appreciate the importance of information theory, familiarity with the information theoretic basics is required, these basics are presented in Chapter 2. In Chapter 3, we use information theory to estimate the amount of …

Approximating The Distribution Of Indefinite Quadratic Forms In Normal Variables By Maximum Entropy Density Estimation, Ghasem Rekabdar, Rahim Chinipardaz

Journal of Modern Applied Statistical Methods

The quadratic form of non-central normal variables is presented based on a sum of weighted independent non-central chi-square variables. This presentation provides moments of quadratic form. The maximum entropy method is used to estimate the density function because distribution moments of quadratic forms are known. A Euclidean distance is proposed to select an appropriate maximum entropy density function. In order to compare with other methods some numerical examples were evaluated. Also, for discrimination between two groups by the Euclidean distances, we obtained a stochastic representation for the linear discriminant function using the quadratic form. The maximum entropy estimation was an …

Semi-Parametric Method To Estimate The Time-To-Failure Distribution And Its Percentiles For Simple Linear Degradation Model, Laila Naji Ba Dakhn, Mohammed Al-Haj Ebrahem, Omar Eidous

Journal of Modern Applied Statistical Methods

Most reliability studies obtained reliability information by using degradation measurements over time, which contains useful data about the product reliability. Parametric methods like the maximum likelihood (ML) estimator and the ordinary least square (OLS) estimator are used widely to estimate the time-to-failure distribution and its percentiles. In this article, we estimate the time-to-failure distribution and its percentiles by using a semi-parametric estimator that assumes the parametric function to have a half- normal distribution or an exponential distribution. The performance of the semi-parametric estimator is compared via simulation study with the ML and OLS estimators by using the mean square error …

Jmasm 48: The Pearson Product-Moment Correlation Coefficient And Adjustment Indices: The Fisher Approximate Unbiased Estimator And The Olkin-Pratt Adjustment (Spss), David A. Walker

Journal of Modern Applied Statistical Methods

This syntax program is intended to provide an application, not readily available, for users in SPSS who are interested in the Pearson product–moment correlation coefficient (r) and r biased adjustment indices such as the Fisher Approximate Unbiased estimator and the Olkin and Pratt adjustment.

Inferential Procedures For Log Logistic Distribution With Doubly Interval Censored Data, Yue Fang Loh, Jayanthi Arasan, Habshah Midi, M. R. Abu Bakar

Journal of Modern Applied Statistical Methods

The log logistic model with doubly interval censored data is examined. Three methods of constructing confidence interval estimates for the parameter of the model were compared and discussed. The results of the coverage probability study indicated that the Wald outperformed the likelihood ratio and jackknife inferential procedures.