Physical Sciences and Mathematics Commons^™

Approximation Multivariate Distribution Of Main Indices Of Tehran Stock Exchange With Pair-Copula, G. Parham, A. Daneshkhah, O. Chatrabgoun

Journal of Modern Applied Statistical Methods

The multivariate distribution of five main indices of Tehran stock exchange is approximated using a pair-copula model. A vine graphical model is used to produce an n-dimensional copula. This is accomplished using a flexible copula called a minimum information (MI) copula as a part of pair-copula construction. Obtained results show that the achieved model has a good level of approximation.

Vol. 12, No. 2 (Full Issue), Jmasm Editors

Journal of Modern Applied Statistical Methods

No abstract provided.

Beta Binomial Regression, Joseph M. Hilbe

Joseph M Hilbe

Monograph on how to construct, interpret and evaluate beta, beta binomial, and zero inflated beta-binomial regression models. Stata and R code used for examples.

Adapting Data Adaptive Methods For Small, But High Dimensional Omic Data: Applications To Gwas/Ewas And More, Sara Kherad Pajouh, Alan E. Hubbard, Martyn T. Smith

U.C. Berkeley Division of Biostatistics Working Paper Series

Exploratory analysis of high dimensional "omics" data has received much attention since the explosion of high-throughput technology allows simultaneous screening of tens of thousands of characteristics (genomics, metabolomics, proteomics, adducts, etc., etc.). Part of this trend has been an increase in the dimension of exposure data in studies of environmental exposure and associated biomarkers. Though some of the general approaches, such as GWAS, are transferable, what has received less focus is 1) how to derive estimation of independent associations in the context of many competing causes, without resorting to a misspecified model, and 2) how to derive accurate small-sample inference …

Testing The Relative Performance Of Data Adaptive Prediction Algorithms: A Generalized Test Of Conditional Risk Differences, Benjamin A. Goldstein, Eric Polley, Farren Briggs, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In statistical medicine comparing the predictability or fit of two models can help to determine whether a set of prognostic variables contains additional information about medical outcomes, or whether one of two different model fits (perhaps based on different algorithms, or different set of variables) should be preferred for clinical use. Clinical medicine has tended to rely on comparisons of clinical metrics like C-statistics and more recently reclassification. Such metrics rely on the outcome being categorical and utilize a specific and often obscure loss function. In classical statistics one can use likelihood ratio tests and information based criterion if the …

Inferences About Parameters Of Trivariate Normal Distribution With Missing Data, Xing Wang

FIU Electronic Theses and Dissertations

Multivariate normal distribution is commonly encountered in any field, a frequent issue is the missing values in practice. The purpose of this research was to estimate the parameters in three-dimensional covariance permutation-symmetric normal distribution with complete data and all possible patterns of incomplete data. In this study, MLE with missing data were derived, and the properties of the MLE as well as the sampling distributions were obtained. A Monte Carlo simulation study was used to evaluate the performance of the considered estimators for both cases when ρ was known and unknown. All results indicated that, compared to estimators in the …

Uniformly Most Powerful Tests For Simultaneously Detecting A Treatment Effect In The Overall Population And At Least One Subpopulation, Michael Rosenblum

Johns Hopkins University, Dept. of Biostatistics Working Papers

After conducting a randomized trial, it is often of interest to determine treatment effects in the overall study population, as well as in certain subpopulations. These subpopulations could be defined by a risk factor or biomarker measured at baseline. We focus on situations where the overall population is partitioned into two predefined subpopulations. When the true average treatment effect for the overall population is positive, it logically follows that it must be positive for at least one subpopulation. We construct new multiple testing procedures that are uniformly most powerful for simultaneously rejecting the overall population null hypothesis and at least …

Trial Designs That Simultaneously Optimize The Population Enrolled And The Treatment Allocation Probabilities, Brandon S. Luber, Michael Rosenblum, Antoine Chambaz

Johns Hopkins University, Dept. of Biostatistics Working Papers

Standard randomized trials may have lower than desired power when the treatment effect is only strong in certain subpopulations. This may occur, for example, in populations with varying disease severities or when subpopulations carry distinct biomarkers and only those who are biomarker positive respond to treatment. To address such situations, we develop a new trial design that combines two types of preplanned rules for updating how the trial is conducted based on data accrued during the trial. The aim is a design with greater overall power and that can better determine subpopulation specific treatment effects, while maintaining strong control of …

Statistical Inference For Data Adaptive Target Parameters, Mark J. Van Der Laan, Alan E. Hubbard, Sara Kherad Pajouh

U.C. Berkeley Division of Biostatistics Working Paper Series

Consider one observes n i.i.d. copies of a random variable with a probability distribution that is known to be an element of a particular statistical model. In order to define our statistical target we partition the sample in V equal size sub-samples, and use this partitioning to define V splits in estimation-sample (one of the V subsamples) and corresponding complementary parameter-generating sample that is used to generate a target parameter. For each of the V parameter-generating samples, we apply an algorithm that maps the sample in a target parameter mapping which represent the statistical target parameter generated by that parameter-generating …

Balancing Score Adjusted Targeted Minimum Loss-Based Estimation, Samuel D. Lendle, Bruce Fireman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Adjusting for a balancing score is sufficient for bias reduction when estimating causal effects including the average treatment effect and effect among the treated. Estimators that adjust for the propensity score in a nonparametric way, such as matching on an estimate of the propensity score, can be consistent when the estimated propensity score is not consistent for the true propensity score but converges to some other balancing score. We call this property the balancing score property, and discuss a class of estimators that have this property. We introduce a targeted minimum loss-based estimator (TMLE) for a treatment specific mean with …

Optimal Tests Of Treatment Effects For The Overall Population And Two Subpopulations In Randomized Trials, Using Sparse Linear Programming, Michael Rosenblum, Han Liu, En-Hsu Yen

Johns Hopkins University, Dept. of Biostatistics Working Papers

We propose new, optimal methods for analyzing randomized trials, when it is suspected that treatment effects may differ in two predefined subpopulations. Such sub-populations could be defined by a biomarker or risk factor measured at baseline. The goal is to simultaneously learn which subpopulations benefit from an experimental treatment, while providing strong control of the familywise Type I error rate. We formalize this as a multiple testing problem and show it is computationally infeasible to solve using existing techniques. Our solution involves a novel approach, in which we first transform the original multiple testing problem into a large, sparse linear …

Estimating Effects On Rare Outcomes: Knowledge Is Power, Laura B. Balzer, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Many of the secondary outcomes in observational studies and randomized trials are rare. Methods for estimating causal effects and associations with rare outcomes, however, are limited, and this represents a missed opportunity for investigation. In this article, we construct a new targeted minimum loss-based estimator (TMLE) for the effect of an exposure or treatment on a rare outcome. We focus on the causal risk difference and statistical models incorporating bounds on the conditional risk of the outcome, given the exposure and covariates. By construction, the proposed estimator constrains the predicted outcomes to respect this model knowledge. Theoretically, this bounding provides …

Estimating Effects On Rare Outcomes: Knowledge Is Power, Laura B. Balzer, Mark J. Van Der Laan

Laura B. Balzer

Many of the secondary outcomes in observational studies and randomized trials are rare. Methods for estimating causal effects and associations with rare outcomes, however, are limited, and this represents a missed opportunity for investigation. In this article, we construct a new targeted minimum loss-based estimator (TMLE) for the effect of an exposure or treatment on a rare outcome. We focus on the causal risk difference and statistical models incorporating bounds on the conditional risk of the outcome, given the exposure and covariates. By construction, the proposed estimator constrains the predicted outcomes to respect this model knowledge. Theoretically, this bounding provides …

The X-Alter Algorithm: A Parameter-Free Method Of Unsupervised Clustering, Thomas Laloë, Rémi Servien

Journal of Modern Applied Statistical Methods

Using quantization techniques, Laloë (2010) defined a new clustering algorithm called Alter. This L¹-based algorithm is shown to be convergent but suffers two major flaws. The number of clusters, K, must be supplied by the user and the computational cost is high. This article adapts the X-means algorithm (Pelleg & Moore, 2000) to solve both problems.

Estimation And Testing In Type I Generalized Half Logistic Distribution, R. R. L. Kantam, V. Ramakrishna, M. S. Ravikumar

Journal of Modern Applied Statistical Methods

A generalization of the half logistic distribution is developed through exponentiation of its cumulative distribution function and termed the Type I Generalized Half Logistic Distribution (GHLD). GHLD’s distributional characteristics and parameter estimation using maximum likelihood and modified maximum likelihood methods are presented with comparisons. Comparison of Type I GHLD and the exponential distribution is conducted via likelihood ratio criterion.

Fitting Proportional Odds Models To Educational Data With Complex Sampling Designs In Ordinal Logistic Regression, Xing Liu, Hari Koirala

Journal of Modern Applied Statistical Methods

The conventional proportional odds (PO) model assumes that data are collected using simple random sampling by which each sampling unit has the equal probability of being selected from a population. However, when complex survey sampling designs are used, such as stratified sampling, clustered sampling or unequal selection probabilities, it is inappropriate to conduct ordinal logistic regression analyses without taking sampling design into account. Failing to do so may lead to biased estimates of parameters and incorrect corresponding variances. This study illustrates the use of PO models with complex survey data to predict mathematics proficiency levels using Stata and compare the …

P-Values Versus Significance Levels, Phillip I. Good

Journal of Modern Applied Statistical Methods

In this article Phillip Good responds to Richard Anderson's article Conceptual Distinction between the Critical p Value and the Type I Error Rate in Permutation Testing.

Conceptual Distinction Between The Critical P Value And The Type I Error Rate In Permutation Testing: Author Response To Peer Comments, Richard B. Anderson

Journal of Modern Applied Statistical Methods

Richard Anderson responds to comments regarding his target article Conceptual Distinction between the Critical p Value and the Type I Error Rate in Permutation Testing.

Randomization Test P-Values Versus Significance Levels, Bryan Manly

Journal of Modern Applied Statistical Methods

Bryan Manly responds to Richard Anderson's article Conceptual Distinction between the Critical p Value and the Type I Error Rate in Permutation Testing.

Using The Bootstrap For Estimating The Sample Size In Statistical Experiments, Maher Qumsiyeh

Journal of Modern Applied Statistical Methods

Efron’s (1979) Bootstrap has been shown to be an effective method for statistical estimation and testing. It provides better estimates than normal approximations for studentized means, least square estimates and many other statistics of interest. It can be used to select the active factors - factors that have an effect on the response - in experimental designs. This article shows that the bootstrap can be used to determine sample size or the number of runs required to achieve a certain confidence level in statistical experiments.

Estimation Of Variance Using Known Coefficient Of Variation And Median Of An Auxiliary Variable, J. Subramani, G. Kumarapandiyan

Journal of Modern Applied Statistical Methods

A modified ratio type variance estimator for estimating population variance of a study variable when the population median and coefficient of variation of an auxiliary variable are known is proposed. The bias and mean squared error of the proposed estimator are derived and conditions under which the proposed estimator performs better than the traditional ratio type variance estimators and modified ratio type variance estimators are obtained. Using a numerical study results show that the proposed estimator performs better than the traditional ratio type variance estimator and existing modified ratio type variance estimators.

A Monte Carlo Simulation Of The Robust Rank-Order Test Under Various Population Symmetry Conditions, William T. Mickelson

Journal of Modern Applied Statistical Methods

The Type I Error Rate of the Robust Rank Order test under various population symmetry conditions is explored through Monte Carlo simulation. Findings indicate the test has difficulty controlling Type I error under generalized Behrens-Fisher conditions for moderately sized samples.

A Response To Anderson's (2013) Conceptual Distinction Between The Critical P Value And Type I Error Rate In Permutation Testing, Fortunato Pesarin, Stefano Bonnini

Journal of Modern Applied Statistical Methods

Pesarin and Bonnini respond to Anderson's (2013) Conceptual Distinction between the Critical p value and Type I Error Rate in Permutation Testing

Conceptual Distinction Between The Critical P Value And The Type I Error Rate In Permutation Testing, Richard B. Anderson

Journal of Modern Applied Statistical Methods

To counter past assertions that permutation testing is not distribution-free, this article clarifies that the critical p value (alpha) in permutation testing is not a Type I error rate and that a test's validity is independent of the concept of Type I error.

The Length-Biased Versus Random Sampling For The Binomial And Poisson Events, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar

Journal of Modern Applied Statistical Methods

The equivalence between the length-biased and the random sampling on a non-negative, discrete random variable is established. The length-biased versions of the binomial and Poisson distributions are discussed.

Constructing A More Powerful Test In Two-Level Block Randomized Designs, Spyros Konstantopoulos

Journal of Modern Applied Statistical Methods

A more powerful test is proposed for the treatment effect in two-level block randomized designs where random assignment takes place at the first level. When clustering at the second level is assumed to be known, the proposed test produces higher estimates of power than the typical test.

Priorities In Thurstone Scaling And Steady-State Probabilities In Markov Stochastic Modeling, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

Thurstone scaling is widely used in marketing and advertising research where various methods of applied psychology are utilized. This article considers several analytical tools useful for positioning a set of items on a Thurstone scale via regression modeling and Markov stochastic processing in the form of Chapman-Kolmogorov equations. These approaches produce interval and ratio scales of preferences and enrich the possibilities of paired comparison estimation applied for solving practical problems of prioritization and probability of choice modeling.

Improved Estimators In Finite Population Surveys: Theory And Applications, Sunil Kumar

Journal of Modern Applied Statistical Methods

Improved estimators are proposed for estimating the population mean Y̅ of the study variable y using auxiliary variable x in simple random sampling. Explicit expression for the bias and MSE of the proposed family are derived to the first order of approximation. The proposed estimators are compared with other estimators and theoretical findings are illustrated by two numerical examples.

On The Gamma-Half Normal Distribution And Its Applications, Ayman Alzaatreh, Kristen Knight

Journal of Modern Applied Statistical Methods

A new distribution, the gamma-half normal distribution, is proposed and studied. Various structural properties of the gamma-half normal distribution are derived. The shape of the distribution may be unimodal or bimodal. Results for moments, limit behavior, mean deviations and Shannon entropy are provided. To estimate the model parameters, the method of maximum likelihood estimation is proposed. Three real-life data sets are used to illustrate the applicability of the gamma-half normal distribution.

An Approach For Dealing With Statuses Of Non-Statistically Significant Interactions Between Treatments, Zakaria M. Sawan

Journal of Modern Applied Statistical Methods

A field experiment on cotton yield resulted in a non-statistically significant interaction. An approach for follow-up examination between treatments based on least significant difference values was suggested to identify the effect regardless of insignificance. It was found that the classical formula used in calculating the significance of interactions suffers a possible shortage that can be eliminated by applying a suggested revision.