Statistical Theory Commons^™

Oracle And Multiple Robustness Properties Of Survey Calibration Estimator In Missing Response Problem, Kwun Chuen Gary Chan

UW Biostatistics Working Paper Series

In the presence of missing response, reweighting the complete case subsample by the inverse of nonmissing probability is both intuitive and easy to implement. However, inverse probability weighting is not efficient in general and is not robust against misspecification of the missing probability model. Calibration was developed by survey statisticians for improving efficiency of inverse probability weighting estimators when population totals of auxiliary variables are known and when inclusion probability is known by design. In missing data problem we can calibrate auxiliary variables in the complete case subsample to the full sample. However, the inclusion probability is unknown in general …

Modification And Improvement Of Empirical Likelihood For Missing Response Problem, Kwun Chuen Gary Chan

UW Biostatistics Working Paper Series

An empirical likelihood (EL) estimator was proposed by Qin and Zhang (2007) for a missing response problem under a missing at random assumption. They showed by simulation studies that the finite sample performance of EL estimator is better than some existing estimators. However, the empirical likelihood estimator does not have a uniformly smaller asymptotic variance than other estimators in general. We consider several modifications to the empirical likelihood estimator and show that the proposed estimator dominates the empirical likelihood estimator and several other existing estimators in terms of asymptotic efficiencies. The proposed estimator also attains the minimum asymptotic variance among …

Modification And Improvement Of Empirical Liklihood For Missing Response Problem, Gary Chan

UW Biostatistics Working Paper Series

An empirical likelihood (EL) estimator was proposed by Qin and Zhang (2007) for a missing response problem under a missing at random assumption. They showed by simulation studies that the finite sample performance of EL estimator is better than some existing estimators. However, the empirical likelihood estimator does not have a uniformly smaller asymptotic variance than other estimators in general. We consider several modifications to the empirical likelihood estimator and show that the proposed estimator dominates the empirical likelihood estimator and several other existing estimators in terms of asymptotic efficiencies. The proposed estimator also attains the minimum asymptotic variance among …

Minimum Description Length Measures Of Evidence For Enrichment, Zhenyu Yang, David R. Bickel

COBRA Preprint Series

In order to functionally interpret differentially expressed genes or other discovered features, researchers seek to detect enrichment in the form of overrepresentation of discovered features associated with a biological process. Most enrichment methods treat the p-value as the measure of evidence using a statistical test such as the binomial test, Fisher's exact test or the hypergeometric test. However, the p-value is not interpretable as a measure of evidence apart from adjustments in light of the sample size. As a measure of evidence supporting one hypothesis over the other, the Bayes factor (BF) overcomes this drawback of the p-value but lacks …

Efficient Measurement Error Correction With Spatially Misaligned Data, Adam A. Szpiro, Lianne Sheppard, Thomas Lumley

UW Biostatistics Working Paper Series

Association studies in environmental statistics often involve exposure and outcome data that are misaligned in space. A common strategy is to employ a spatial model such as universal kriging to predict exposures at locations with outcome data and then estimate a regression parameter of interest using the predicted exposures. This results in measurement error because the predicted exposures do not correspond exactly to the true values. We characterize the measurement error by decomposing it into Berkson-like and classical-like components. One correction approach is the parametric bootstrap, which is effective but computationally intensive since it requires solving a nonlinear optimization problem …

Minimum Description Length And Empirical Bayes Methods Of Identifying Snps Associated With Disease, Ye Yang, David R. Bickel

COBRA Preprint Series

The goal of determining which of hundreds of thousands of SNPs are associated with disease poses one of the most challenging multiple testing problems. Using the empirical Bayes approach, the local false discovery rate (LFDR) estimated using popular semiparametric models has enjoyed success in simultaneous inference. However, the estimated LFDR can be biased because the semiparametric approach tends to overestimate the proportion of the non-associated single nucleotide polymorphisms (SNPs). One of the negative consequences is that, like conventional p-values, such LFDR estimates cannot quantify the amount of information in the data that favors the null hypothesis of no disease-association.

We …

Improving The Power Of Chronic Disease Surveillance By Incorporating Residential History, Justin Manjourides, Marcello Pagano

Harvard University Biostatistics Working Paper Series

No abstract provided.

Generalized Variances Ratio Test For Comparing K Covariance Matrices From Dependent Normal Populations, Marcelo Angelo Cirillo, Daniel Furtado Ferreira, Thelma Sáfadi, Eric Batista Ferreira

Journal of Modern Applied Statistical Methods

New tests based on the ratio of generalized variances are presented to compare covariance matrices from dependent normal populations. Monte Carlo simulation concluded that the tests considered controlled the Type I error, providing empirical probabilities that were consistent with the nominal level stipulated.

A Ga-Based Sales Forecasting Model Incorporating Promotion Factors, Li-Chih Wang, Chin-Lien Wang

Journal of Modern Applied Statistical Methods

Because promotions are critical factors highly related to product sales of consumer packaged goods (CPG) companies, predictors concerning sales forecast of CPG products must take promotions into consideration. Decomposition regression incorporating contextual factors offers a method for exploiting both reliability of statistical forecasting and flexibility of judgmental forecasting employing domain knowledge. However, it suffers from collinearity causing poor performance in variable identification and parameter estimation with traditional ordinary least square (OLS). Empirical research evidence shows that - in the case of collinearity - in variable identification, parameter estimation, and out of sample forecasting, genetic algorithms (GA) as an estimator outperform …

Estimating The Non-Existent Mean And Variance Of The F-Distribution By Simulation, Hamid Reza Kamali, Parisa Shahnazari-Shahrezaei

Journal of Modern Applied Statistical Methods

In theory, all moments of some probability distributions do not necessarily exist. In the other words, they may be infinite or undefined. One of these distributions is the F-distribution whose mean and variance have not been defined for the second degree of freedom less than 3 and 5, respectively. In some cases, a large statistical population having an F-distribution may exist and the aim is to obtain its mean and variance which are an estimation of the non-existent mean and variance of F-distribution. This article considers a large sample F-distribution to estimate its non-existent mean and variance using Simul8 simulation …

Ridge Regression Based On Some Robust Estimators, Hatice Samkar, Ozlem Alpu

Journal of Modern Applied Statistical Methods

Robust ridge methods based on M, S, MM and GM estimators are examined in the presence of multicollinearity and outliers. GMWalker, using the LS estimator as the initial estimator is used. S and MM estimators are also used as initial estimators with the aim of evaluating the two alternatives as biased robust methods.

A Flexible Method For Testing Independence In Two-Way Contingency Tables, Peyman Jafari, Noori Akhtar-Danesh, Zahra Bagheri

Journal of Modern Applied Statistical Methods

A flexible approach for testing association in two-way contingency tables is presented. It is simple, does not assume a specific form for the association and is applicable to tables with nominal-by-nominal, nominal-by-ordinal, and ordinal-by-ordinal classifications.

Statistical And Mathematical Modeling Versus Nhst? There’S No Competition!, Joseph Lee Rodgers

Journal of Modern Applied Statistical Methods

Some of Robinson & Levin’s critique of Rodgers (2010) is cogent, helpful, and insightful – although limiting. Recent methodology has advanced through the development of structural equation modeling, multi-level modeling, missing data methods, hierarchical linear modeling, categorical data analysis, as well as the development of many dedicated and specific behavioral models. These methodological approaches are based on a revised epistemological system, and have emerged naturally, without the need for task forces, or even much self-conscious discussion. The original goal was neither to develop nor promote a modeling revolution. That has occurred; I documented its development and its status. Two organizing …

Effect Of Measurement Errors On The Separate And Combined Ratio And Product Estimators In Stratified Random Sampling, Housila P. Singh, Namrata Karpe

Journal of Modern Applied Statistical Methods

Separate and combined ratio, product and difference estimators are introduced for population mean μ_Y of a study variable Y using auxiliary variable X in stratified sampling when the observations are contaminated with measurement errors. The bias and mean squared error of the proposed estimators have been derived under large sample approximation and their properties are analyzed. Generalized versions of these estimators are given along with their properties.

Recommended Sample Size For Conducting Exploratory Factor Analysis On Dichotomous Data, Robert H. Pearson, Daniel J. Mundform

Journal of Modern Applied Statistical Methods

Minimum sample sizes are recommended for conducting exploratory factor analysis on dichotomous data. A Monte Carlo simulation was conducted, varying the level of communalities, number of factors, variable-to-factor ratio and dichotomization threshold. Sample sizes were identified based on congruence between rotated population and sample factor loadings.

Incidence And Prevalence For A Triply Censored Data, Hilmi F. Kittani

Journal of Modern Applied Statistical Methods

The model introduced for the natural history of a progressive disease has four disease states which are expressed as a joint distribution of three survival random variables. Covariates are included in the model using Cox’s proportional hazards model with necessary assumptions needed. Effects of the covariates are estimated and tested. Formulas for incidence in the preclinical, clinical and death states are obtained, and prevalence formulas are obtained for the preclinical and clinical states. Estimates of the sojourn times in the preclinical and clinical states are obtained.

Robust Estimators In Logistic Regression: A Comparative Simulation Study, Sanizah Ahmad, Norazan Mohamed Ramli, Habshah Midi

Journal of Modern Applied Statistical Methods

The maximum likelihood estimator (MLE) is commonly used to estimate the parameters of logistic regression models due to its efficiency under a parametric model. However, evidence has shown the MLE has an unduly effect on the parameter estimates in the presence of outliers. Robust methods are put forward to rectify this problem. This article examines the performance of the MLE and four existing robust estimators under different outlier patterns, which are investigated by real data sets and Monte Carlo simulation.

Use Of Two Variables Having Common Mean To Improve The Bar-Lev, Bobovitch And Boukai Randomized Response Model, Oluseun Odumade, Sarjinder Singh

Journal of Modern Applied Statistical Methods

A new method to improve the randomized response model due to Bar-Lev, Bobovitch and Boukai (2004) is suggested. It has been observed that if two sensitive (or non sensitive) variables exist that are related to the main study sensitive variable, then those variables could be used to construct ratio type adjustments to the usual estimator of the population mean of a sensitive variable due to Bar-Lev, Bobovitch and Boukai (2004).The relative efficiency of the proposed estimators is studied with respect to the Bar-Lev, Bobovitch and Boukai (2004) models under different situations.

Maximum Downside Semi Deviation Stochastic Programming For Portfolio Optimization Problem, Anton Abdulbasah Kamil, Khlipah Ibrahim

Journal of Modern Applied Statistical Methods

Portfolio optimization is an important research field in financial decision making. The chief character within optimization problems is the uncertainty of future returns. Probabilistic methods are used alongside optimization techniques. Markowitz (1952, 1959) introduced the concept of risk into the problem and used a mean-variance model to identify risk with the volatility (variance) of the random objective. The mean-risk optimization paradigm has since been expanded extensively both theoretically and computationally. A single stage and two stage stochastic programming model with recourse are presented for risk averse investors with the objective of minimizing the maximum downside semideviation. The models employ the …

On Bayesian Shrinkage Setup For Item Failure Data Under A Family Of Life Testing Distribution, Gyan Prakash

Journal of Modern Applied Statistical Methods

Properties of the Bayes shrinkage estimator for the parameter are studied of a family of probability density function when item failure data are available. The symmetric and asymmetric loss functions are considered for two different prior distributions. In addition, the Bayes estimates of reliability function and hazard rate are obtained and their properties are studied.

Bayesian Analysis Of Location-Scale Family Of Distributions Using S-Plus And R Software, Sheikh Parvaiz Ahmad, Aquil Ahmed, Athar Ali Khan

Journal of Modern Applied Statistical Methods

The Normal and Laplace’s methods of approximation for posterior density based on the location-scale family of distributions in terms of the numerical and graphical simulation are examined using S-PLUS and R Software.

Empirical Characteristic Function Approach To Goodness Of Fit Tests For The Logistic Distribution Under Srs And Rss, M. T. Alodat, S. A. Al-Subh, Kamaruzaman Ibrahim, Abdul Aziz Jemain

Journal of Modern Applied Statistical Methods

The integral of the squares modulus of the difference between the empirical characteristic function and the characteristic function of the hypothesized distribution is used by Wong and Sim (2000) to test for goodness of fit. A weighted version of Wong and Sim (2000) under ranked set sampling, a sampling technique introduced by McIntyre (1952), is examined. Simulations that show the ranked set sampling counterpart of Wong and Sim (2000) is more powerful.

Bayesian Analysis For Component Manufacturing Processes, L. V. Nandakishore

Journal of Modern Applied Statistical Methods

In manufacturing processes various machines are used to produce the same product. Based on the age, make, etc., of the machines the output may not always follow the same distribution. An attempt is made to introduce Bayesian techniques for a two machine problem. Two cases are presented in this article.

Neighbor Balanced Block Designs For Two Factors, Seema Jaggi, Cini Varghese, N. R. Abeynayake

Journal of Modern Applied Statistical Methods

The concept of Neighbor Balanced Block (NBB) designs is defined for the experimental situation where the treatments are combinations of levels of two factors and only one of the factors exhibits a neighbor effect. Methods of constructing complete NBB designs for two factors in a plot that is strongly neighbor balanced for one factor are obtained. These designs are variance balanced for estimating the direct effects of contrasts pertaining to combinations of levels of both the factors. An incomplete NBB design for two factors is also presented and is found to be partially variance balanced with three associate classes.

Ann Forecasting Models For Ise National-100 Index, Ozer Ozdemir, Atilla Aslanargun, Senay Asma

Journal of Modern Applied Statistical Methods

Prediction of the outputs of real world systems with accuracy and high speed is crucial in financial analysis due to its effects on worldwide economics. Because the inputs of the financial systems are timevarying functions, the development of algorithms and methods for modeling such systems cannot be neglected. The most appropriate forecasting model for the ISE national-100 index was investigated. Box- Jenkins autoregressive integrated moving average (ARIMA) and artificial neural networks (ANN) are considered by using several evaluations. Results showed that the ANN model with linear architecture better fits the candidate data.

Markov Chain Analysis And Student Academic Progress: An Empirical Comparative Study, Shafiqah Alawadhi, Mokhtar Konsowa

Journal of Modern Applied Statistical Methods

An application of Markov Chain Analysis of student flow at Kuwait University is presented based on a random sample of 1,100 students from the academic years 1996-1997 to 2004-2005. Results were obtained for each college and in total which allows for a comparative study. The students’ mean lifetimes in different levels of study in the colleges as well as the percentage of dropping out of the system are estimated.

Reducing Selection Bias In Analyzing Longitudinal Health Data With High Mortality Rates, Xian Liu, Charles C. Engel, Han Kang, Kristie L. Gore

Journal of Modern Applied Statistical Methods

Two longitudinal regression models, one parametric and one nonparametric, are developed to reduce selection bias when analyzing longitudinal health data with high mortality rates. The parametric mixed model is a two-step linear regression approach, whereas the nonparametric mixed-effects regression model uses a retransformation method to handle random errors across time.

The Not-So-Quiet Revolution: Cautionary Comments On The Rejection Of Hypothesis Testing In Favor Of A “Causal” Modeling Alternative, Daniel H. Robinson, Joel R. Levin

Journal of Modern Applied Statistical Methods

Rodgers (2010) recently applauded a revolution involving the increased use of statistical modeling techniques. It is argued that such use may have a downside, citing empirical evidence in educational psychology that modeling techniques are often applied in cross-sectional, correlational studies to produce unjustified causal conclusions and prescriptive statements.

Notes On Hypothesis Testing Under A Single-Stage Design In Phase Ii Trial, Kung-Jong Lui

Journal of Modern Applied Statistical Methods

A primary objective of a phase II trial is to determine future development is warranted for a new treatment based on whether it has sufficient activity against a specified type of tumor. Limitations exist in the commonly-used hypothesis setting and the standard test procedure for a phase II trial. This study reformats the hypothesis setting to mirror the clinical decision process in practice. Under the proposed hypothesis setting, the critical points and the minimum required sample size for a desired power of finding a superior treatment at a given α -level are presented. An example is provided to illustrate how …

Adjusted Confidence Interval For The Population Median Of The Exponential Distribution, Moustafa Omar Ahmed Abu-Shawiesh

Journal of Modern Applied Statistical Methods

The median confidence interval is useful for one parameter families, such as the exponential distribution, and it may not need to be adjusted if censored observations are present. In this article, two estimators for the median of the exponential distribution, MD, are considered and compared based on the sample median and the maximum likelihood method. The first estimator is the sample median, MD₁, and the second estimator is the maximum likelihood estimator of the median, MD_MLE. Both estimators are used to propose a modified confidence interval for the population median of the exponential distribution, MD …