Statistics and Probability Commons^™

A Proficient Two-Stage Stratified Randomized Response Strategy, Tanveer A. Tarray, Housila P. Singh

Journal of Modern Applied Statistical Methods

A stratified randomized response model based on R. Singh, Singh, Mangat, and Tracy (1995) improved two-stage randomized response strategy is proposed. It has an optimal allocation and large gain in precision. Conditions are obtained under which the proposed model is more efficient than R. Singh et al. (1995) and H. P. Singh and Tarray (2015) models. Numerical illustrations are also given in support of the present study.

Extended Method For Several Dichotomous Covariates To Estimate The Instantaneous Risk Function Of The Aalen Additive Model, Luciane Teixeira Passos Giarola, Mario Javier Ferrua Vivanco, Marcelo Angelo Cirillo, Fortunato Silva Menezes

Journal of Modern Applied Statistical Methods

The instantaneous risk function of Aalen’s model is estimated considering dichotomous covariates, using parametric accumulated risk functions to smooth cumulative risk of Aalen by grouping the individuals into sets named parcels. This methodology can be used for data with dichotomous covariates.

Simple Unbalanced Ranked Set Sampling For Mean Estimation Of Response Variable Of Developmental Programs, Girish Chandra, Dinesh S. Bhoj, Rajiv Pandey

Journal of Modern Applied Statistical Methods

An unbalanced ranked set sampling (RSS) procedure on the skewed survey variable is proposed to estimate the population mean of a response variable from the area of developmental programs which are generally implemented under different phases. It is based on the unbalanced RSS under linear impacts of the program and is compared with the estimators based on simple random sampling (SRS) and balanced RSS. It is shown that the relative precision of the proposed estimator is higher than those of the estimators based on SRS and balanced RSS for three chosen skewed distributions of survey variables.

The Impact Of Sample Size In Cross-Classified Multiple Membership Multilevel Models, Hyewon Chung, Jiseon Kim, Ryoungsun Park, Hyeonjeong Jean

Journal of Modern Applied Statistical Methods

A simulation study was conducted to examine parameter recovery in a cross-classified multiple membership multilevel model. No substantial relative bias was identified for the fixed effect or level-one variance component estimates. However, the level-two cross-classification multiple membership factor variance components were substantially biased with relatively fewer groups.

Bias Assessment And Reduction In Kernel Smoothing, Wenkai Ma

Electronic Thesis and Dissertation Repository

When performing local polynomial regression (LPR) with kernel smoothing, the choice of the smoothing parameter, or bandwidth, is critical. The performance of the method is often evaluated using the Mean Square Error (MSE). Bias and variance are two components of MSE. Kernel methods are known to exhibit varying degrees of bias. Boundary effects and data sparsity issues are two potential problems to watch for. There is a need for a tool to visually assess the potential bias when applying kernel smooths to a given scatterplot of data. In this dissertation, we propose pointwise confidence intervals for bias and demonstrate a …

Using Cyclical Components To Improve The Forecasts Of The Stock Market And Macroeconomic Variables, Kenneth R. Szulczyk, Shibley Sadique

Journal of Modern Applied Statistical Methods

Economic variables such as stock market indices, interest rates, and national output measures contain cyclical components. Forecasting methods excluding these cyclical components yield inaccurate out-of-sample forecasts. Accordingly, a three-stage procedure is developed to estimate a vector autoregression (VAR) with cyclical components. A Monte Carlo simulation shows the procedure estimates the parameters accurately. Subsequently, a VAR with cyclical components improves the root-mean-square error of out-of-sample forecasts by 50% for a stock market model with macroeconomic variables.

Comparison Of Multiple Imputation Methods For Categorical Survey Items With High Missing Rates: Application To The Family Life, Activity, Sun, Health And Eating (Flashe) Study, Benmei Liu, Erin Hennessy, April Oh, Laura A. Dwyer, Linda Nebeling

Journal of Modern Applied Statistical Methods

Two multiple imputation methods, the Sequential Regression Multivariate Imputation Algorithm and the Cox-Lannacchione Weighted Sequential Hotdeck, were examined and compared to impute highly missing categorical variables from the Family Life, Activity, Sun, Health and Eating (FLASHE) study. This paper describes the imputation approaches and results from the study.

Dealing With Sensitive Quantitative Variables: A Comparison Of Sampling Designs For The Procedure Of Gupta And Thornton, Carlos Narciso Bouza Herrera, Prayas Sharma

Journal of Modern Applied Statistical Methods

The use of randomized response procedures allows diminishing the number of non-responses and increasing the accuracy of the responses. A new sampling strategy is developed where the reports are scrambled using the procedure of Gupta and Thornton. The estimator of the mean as well as the errors are developed for the Rao-Hartley-Cochran and Ranked Sets Sampling designs. The proposals are compared with the original model based on the use of simple random sampling.

Bayesian And Semi-Bayesian Estimation Of The Parameters Of Generalized Inverse Weibull Distribution, Kamaljit Kaur, Kalpana K. Mahajan, Sangeeta Arora

Journal of Modern Applied Statistical Methods

Bayesian and semi-Bayesian estimators of parameters of the generalized inverse Weibull distribution are obtained using Jeffreys’ prior and informative prior under specific assumptions of loss function. Using simulation, the relative efficiency of the proposed estimators is obtained under different set-ups. A real life example is also given.

Overcoming Small Data Limitations In Heart Disease Prediction By Using Surrogate Data, Alfeo Sabay, Laurie Harris, Vivek Bejugama, Karen Jaceldo-Siegl

SMU Data Science Review

In this paper, we present a heart disease prediction use case showing how synthetic data can be used to address privacy concerns and overcome constraints inherent in small medical research data sets. While advanced machine learning algorithms, such as neural networks models, can be implemented to improve prediction accuracy, these require very large data sets which are often not available in medical or clinical research. We examine the use of surrogate data sets comprised of synthetic observations for modeling heart disease prediction. We generate surrogate data, based on the characteristics of original observations, and compare prediction accuracy results achieved from …

Minimizing The Perceived Financial Burden Due To Cancer, Hassan Azhar, Zoheb Allam, Gino Varghese, Daniel W. Engels, Sajiny John

SMU Data Science Review

In this paper, we present a regression model that predicts perceived financial burden that a cancer patient experiences in the treatment and management of the disease. Cancer patients do not fully understand the burden associated with the cost of cancer, and their lack of understanding can increase the difficulties associated with living with the disease, in particular coping with the cost. The relationship between demographic characteristics and financial burden were examined in order to better understand the characteristics of a cancer patient and their burden, while all subsets regression was used to determine the best predictors of financial burden. Age, …

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.

Asymptotic Behavior Of The Random Logistic Model And Of Parallel Bayesian Logspline Density Estimators, Konstandinos Kotsiopoulos

Doctoral Dissertations

This dissertation is comprised of two separate projects. The first concerns a Markov chain called the Random Logistic Model. For r in (0,4] and x in [0,1] the logistic map f_r(x) = rx(1 - x) defines, for positive integer t, the dynamical system x_r(t + 1) = f(x_r(t)) on [0,1], where x_r(1) = x. The interplay between this dynamical system and the Markov chain x_r,N(t) defined by perturbing the logistic map by truncated Gaussian noise scaled by N^-1/2, where N -> infinity, is studied. A natural question is …

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 …

Regression Analysis For Ordinal Outcomes In Matched Study Design: Applications To Alzheimer's Disease Studies, Elizabeth Austin

Masters Theses

Alzheimer's Disease (AD) affects nearly 5.4 million Americans as of 2016 and is the most common form of dementia. The disease is characterized by the presence of neurofibrillary tangles and amyloid plaques [1]. The amount of plaques are measured by Braak stage, post-mortem. It is known that AD is positively associated with hypercholesterolemia [16]. As statins are the most widely used cholesterol-lowering drug, there may be associations between statin use and AD. We hypothesize that those who use statins, specifically lipophilic statins, are more likely to have a low Braak stage in post-mortem analysis.

In order to address this hypothesis, …

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.

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).

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.

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.

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 …

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.

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 …