Statistical Theory Commons^™

How Good Is Best? Multivariate Case Of Ehrenberg-Weisberg Analysis Of Residual Errors In Competing Regressions, Stan Lipovetsky

Journal of Modern Applied Statistical Methods

A.S.C. Ehrenberg first noticed and S. Weisberg then formalized a property of pairwise regression to keep its quality almost at the same level of precision while the coefficients of the model could vary over a wide span of values. This paper generalizes the estimates of the percent change in the residual standard deviation to the case of competing multiple regressions. It shows that in contrast to the simple pairwise model, the coefficients of multiple regression can be changed over a wider range of the values including the opposite by signs coefficients. Consideration of these features facilitates better understanding the properties …

Comparison Of Three Calculation Methods For A Bayesian Inference Of P(Π1 > Π2), Yohei Kawasaki, Asanao Shimokawa, Etsuo Miyaoka

Journal of Modern Applied Statistical Methods

In Bayesian inference, some researchers have examined the difference of binominal proportions using θ = P(π₁ > π₂ − Δ₀|X₁,X₂), where X_i denote binomial random variable with parameter π_i. An approximate method and the MCMC method are compared with an exact method for θ, and results of actual clinical trials using θ are presented.

Parameter Estimations Based On Kumaraswamy Progressive Type Ii Censored Data With Random Removals, Navid Feroze, Ibrahim El-Batal

Journal of Modern Applied Statistical Methods

The estimation of two parameters of the Kumaraswamy distribution is considered under Type II progressive censoring with random removals, where the number of units removed at each failure time has a binomial distribution. The MLE was used to obtain the estimators of the unknown parameters, and the asymptotic variance - covariance matrix was also obtained. The formula to compute the expected test time was derived. A numerical study was carried out for different combinations of model parameters. Different censoring schemes were used for the estimation, and performance of these schemes was compared.

Akaike Information Criterion To Select The Parametric Detection Function For Kernel Estimator Using Line Transect Data, Omar Eidous, Samar Al-Salman

Journal of Modern Applied Statistical Methods

Among different candidate parametric detection functions, it is suggested to use Akaike Information Criterion (AIC) to select the most appropriate one of them to fit line transect data. Four different detection functions are considered in this paper. Two of them are taken to satisfy the shoulder condition assumption and the other two estimators do not satisfy this condition. Once the appropriate detection function is determined, it also can be used to select the smoothing parameter of the nonparametric kernel estimator. For a wide range of target densities, a simulation results show the reasonable and good performances of the …

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

Journal of Modern Applied Statistical Methods

No abstract provided.

Constructing Confidence Intervals For Effect Sizes In Anova Designs, Li-Ting Chen, Chao-Ying Joanne Peng

Journal of Modern Applied Statistical Methods

A confidence interval for effect sizes provides a range of plausible population effect sizes (ES) that are consistent with data. This article defines an ES as a standardized linear contrast of means. The noncentral method, Bonett’s method, and the bias-corrected and accelerated bootstrap method are illustrated for constructing the confidence interval for such an effect size. Results obtained from the three methods are discussed and interpretations of results are offered.

Bayesian Joinpoint Regression Model For Childhood Brain Cancer Mortality, Ram C. Kafle, Netra Khanal, Chris P. Tsokos

Journal of Modern Applied Statistical Methods

The Bayesian approach of joinpoint regression is widely used to analyze trends in cancer mortality, incidence and survival data. The Bayesian joinpoint regression model was used to study the childhood brain cancer mortality rate and its average percentage change (APC) per year. Annual observed mortality counts of children ages 0-19 from 1969-2009 obtained from Surveillance Epidemiology and End Results (SEER) database of National Cancer Institute (NCI) were analyzed. It was assumed that death counts are probabilistically characterized by the Poisson distribution and they were modeled using log link function. Results were compared with the mortality trend obtained using joinpoint software …

On Comparison Of Exponential And Hyperbolic Exponential Growth Models In Height/Diameter Increment Of Pines (Pinus Caribaea), S. O. Oyamakin, A. U. Chukwu, T. A. Bamiduro

Journal of Modern Applied Statistical Methods

A new tree growth model called the hyperbolic exponential nonlinear growth model is suggested. Its ability in model prediction was compared with the Malthus or exponential growth model an approach which mimicked the natural variability of heights/diameter increment with respect to age and therefore provides more realistic height/diameter predictions as demonstrated by the results of the Kolmogorov Smirnov test and Shapiro-Wilk test. The mean function of top height/Dbh over age using the two models under study predicted closely the observed values of top height/Dbh in the Hyperbolic exponential nonlinear growth models better than the ordinary exponential growth model without violating …

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 …

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 …

An Alternative Approach To Reduce Dimensionality In Data Envelopment Analysis, Grace Lee Ching Yap, Wan Rosmanira Ismail, Zaidi Isa

Journal of Modern Applied Statistical Methods

Principal component analysis reduces dimensionality; however, uncorrelated components imply the existence of variables with weights of opposite signs. This complicates the application in data envelopment analysis. To overcome problems due to signs, a modification to the component axes is proposed and was verified using Monte Carlo simulations.

Robustness Of Dewma Versus Ewma Control Charts To Non-Normal Processes, Saad Saeed Alkahtani

Journal of Modern Applied Statistical Methods

Exponentially weighted moving average (EWMA) and double EWMA (DEWMA) control charts were designed under the normality assumption. This study considers various skewed (Gamma) and symmetric non-normal (t) distributions to examine the effect of non-normality on the average run length (ARL) performance of EWMA and DEWMA. ARL performances were investigated and compared using Monte Carlo simulations. Results show that DEWMA charts can be designed to be robust to non-normality, that the ARL performances of EWMA and DEWMA charts were more robust to t distributions and DEWMA was more robust to non-normality for larger values of the smoothing parameter.

An Approximate Approach To The Economic Design Of X̅ Charts By Considering The Cost Of Quality, M. A. A. Cox

Journal of Modern Applied Statistical Methods

The selection of three parameters {h,k,n} is necessary to design a x̅ control chart. A cost model employing a Burr distribution is examined. Previously employed methods are refined and extended. A series of approximations are proposed that enable a rapid parameter selection. It is hoped that reducing the computational complexity of previous approaches will lead to wider utilization of x̅ control charts.

Modeling And Handling Overdispersion Health Science Data With Zero-Inflated Poisson Model, Nur Syabiha Binti Zafakali, Wan Muhamad Amir Bin W Ahmad

Journal of Modern Applied Statistical Methods

Health sciences research often involves analyses of repeated measurement or longitudinal count data analyses that exhibit excess zeros. Overdispersion occurs when count data measurements have greater variability than allowed. This phenomenon can be carried over to zero-inflated count data modeling. Referred to as zero-inflation, the Zero-Inflated Poisson (ZIP) model can be used to model such data. The Zero-Inflated Negative Binomial (ZINB) model is used to account for overdispersion detected in count data. The ZINB model is considered as an alternative for the Zero-Inflated Generalized Poisson (ZIGP) model for zero-inflated overdispersed count data. Consequently, zero-inflated models have been proposed for the …

A Note On Α-Curvature Of The Manifolds Of The Length-Biased Lognormal And Gamma Distributions In View Of Related Applications In Data Analysis, Makarand V. Ratnaparkhi, Uttara V. Naik-Nimbalkar

Journal of Modern Applied Statistical Methods

The α-curvature tensors of the statistical manifolds of the length-biased versions of the log-normal and gamma distributions are derived and discussed. This study was designed to investigate observations related to the parameter estimation for the length-biased lognormal distribution as a model for the lengthbiased data from oil field exploration.

The Probit Link Function In Generalized Linear Models For Data Mining Applications, Mehdi Razzaghi

Journal of Modern Applied Statistical Methods

The use of logistic regression for outcome classification of dichotomous variables is well known in data mining applications. The estimated probability of the logit transformation belongs to the class of canonical link functions that follow from particular probability distribution functions. A closely related model is the probit link which can be used for binary responses. Although the probit link is not canonical, in some cases the overall fit of the model can be improved by using non-canonical link functions. This article reviews the properties of the probit link function and discusses its applications in data mining problems. Contrasts and comparisons …

Parameter Estimation Of A Class Of Hidden Markov Model With Diagnostics, E. B. Nkemnole, O. Abass, R. A. Kasumu

Journal of Modern Applied Statistical Methods

A stochastic volatility (SV) problem is formulated as a state space form of a Hidden Markov model (HMM). The SV model assumes that the distribution of asset returns conditional on the latent volatility is normal. This article analyzes the SV model with the student-t distribution and the generalized error distribution (GED) and compares these distributions with a mixture of normal distributions from Kim and Stoffer (2008). A Sequential Monte Carlo with Expectation Maximization (SMCEM) algorithm technique was used to estimate parameters for the extended volatility model; the Akaike Information Criteria (AIC) and forecast statistics were calculated to compare distribution fit. …

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.

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.

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.

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.

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.

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.

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.