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Estimation Of Cumulative Incidence Functions In Competing Risks Studies Under An Order Restriction, Hammou El Barmi, Subhash C. Kochar, Hari Mukerjee, Francisco J. Samaniego

Mathematics and Statistics Faculty Publications and Presentations

In the competing risks problem an important role is played by the cumulative incidence function (CIF), whose value at time t is the probability of failure by time t for a particular type of failure in the presence of other risks. Its estimation and asymptotic distribution theory have been studied by many. In some cases there are reasons to believe that the CIFs due to two types of failure are order restricted. Several procedures have appeared in the literature for testing for such orders. In this paper we initiate the study of estimation of two CIFs subject to a type …

How Employment-Discrimination Plaintiffs Fare In The Federal Courts Of Appeals, Kevin M. Clermont, Theodore Eisenberg, Stewart J. Schwab

Cornell Law Faculty Publications

Employment-discrimination plaintiffs swim against the tide. Compared to the typical plaintiff, they win a lower proportion of cases during pretrial and after trial. Then, many of their successful cases are appealed. On appeal, they have a harder time in upholding their successes, as well in reversing adverse outcome.

This tough story does not describe some tiny corner of the litigation world. Employment-discrimination cases constitute an increasing fraction of the federal civil docket, now reigning as the largest single category of cases at nearly 10 percent.

In this article, we use official government data to describe the appellate phase of this …

Sibling Recurrence Risk Ratio Analysis Of The Metabolic Syndrome And Its Components Over Time., Wei J. Chen, Pi Hua Liu, Yen Yi Ho, Kuo Liong Chien, Min Tzu Lo, Wei Liang Shih, Yu Chun Yen, Wen Chung Lee

Faculty Publications

The purpose of this study was to estimate both cross-sectional sibling recurrence risk ratio (lambdas) and lifetime lambdas for the metabolic syndrome and its individual components over time among sibships in the prospectively followed-up cohorts provided by the Genetic Analysis Workshop 13. Five measures included in the operational criteria of the metabolic syndrome by the Adult Treatment Panel III were examined. A method for estimating sibling recurrence risk with correction for complete ascertainment was used to estimate the numerator, and the prevalence in the whole cohort was used as the denominator of lambdas. Considerable variability in the lambdas was found …

Applications Of Recursive Estimation Methods In Statistical Process Control, Shelton Peiris, Aerambamoorthy Thavaneswaran, David E. Allen, R. Mellor

Research outputs pre 2011

In recent years there has been a growing interest in recursive estimation techniques as applied to statistical process control (SPC). In cases where prior information about the processes are available, it is shown that procedures based on the “optimal” smoothing can be superior to the classical procedures like Shewhart’s CUSUM control charts (see, for instance, Thavaneswaran, McPherson and Abraham (1998)). This paper reviews the recursive algorithms based on EWMA (exponentially weighted moving average), DLM (dynamic linear modeling), KF (Kalman filtering) and OS (optimal smoothing) in statistical process control with correlated data. We also discuss various relationships among the asymptotic mean …

Some Evidence On The Information Content Of Undisclosed Limit Orders On The Asx, M. Aitken, David E. Allen, Wenling J. Yang

Research outputs pre 2011

This paper is concerned with investigating the information content of undisclosed limit orders, and identifying factors that affect their size, plus the examination of the brokers’ behaviour in using undisclosed orders. We adopt a sample of liquid stocks listed on the ASX, and our estimation results indicate that the size of undisclosed orders are affected by a number of factors. Given the ‘stealth trading’ pattern of behaviour observed in large disclosed orders, this paper provides evidence to support a similar pattern of behaviour in the case of undisclosed orders. Our model also provides an appropriate measure for estimating the size …

Normal Mixture Models For Gene Cluster Identification In Two Dimensional Microarray Data, Eric Scott Harvey

Theses and Dissertations

This dissertation focuses on methodology specific to microarray data analyses that organize the data in preliminary steps and proposes a cluster analysis method which improves the interpretability of the cluster results. Cluster analysis of microarray data allows samples with similar gene expression values to be discovered and may serve as a useful diagnostic tool. Since microarray data is inherently noisy, data preprocessing steps including smoothing and filtering are discussed. Comparing the results of different clustering methods is complicated by the arbitrariness of the cluster labels. Methods for re-labeling clusters to assess the agreement between the results of different clustering techniques …

Invariant Sets And Inverse Limits, William Thomas Ingram

Mathematics and Statistics Faculty Research & Creative Works

In this paper we investigate the nature of inverse limits from the point of view of invariant sets. We then introduce a special class of examples of inverse limits on [0,1] using Markov bonding maps determined by members of the group of permutations on n elements. © 2002 Elsevier Science B.V. All rights reserved.

Recurrent Events Analysis In The Presence Of Time Dependent Covariates And Dependent Censoring, Maja Miloslavsky, Sunduz Keles, Mark J. Van Der Laan, Steve Butler

U.C. Berkeley Division of Biostatistics Working Paper Series

Recurrent events models have lately received a lot of attention in the literature. The majority of approaches discussed show the consistency of parameter estimates under the assumption that censoring is independent of the recurrent events process of interest conditional on the covariates included into the model. We provide an overview of available recurrent events analysis methods, and present an inverse probability of censoring weighted estimator for the regression parameters in the Andersen-Gill model that is commonly used for recurrent event analysis. This estimator remains consistent under informative censoring if the censoring mechanism is estimated consistently, and generally improves on the …

Construction Of Counterfactuals And The G-Computation Formula, Zhuo Yu, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Robins' causal inference theory assumes existence of treatment specific counterfactual variables so that the observed data augmented by the counterfactual data will satisfy a consistency and a randomization assumption. Gill and Robins [2001] show that the consistency and randomization assumptions do not add any restrictions to the observed data distribution. In particular, they provide a construction of counterfactuals as a function of the observed data distribution. In this paper we provide a construction of counterfactuals as a function of the observed data itself. Our construction provides a new statistical tool for estimation of counterfactual distributions. Robins [1987b] shows that the …

On Choosing And Bounding Probability Metrics, Alison L. Gibbs, Francis E. Su

All HMC Faculty Publications and Research

When studying convergence of measures, an important issue is the choice of probability metric. We provide a summary and some new results concerning bounds among some important probability metrics/distances that are used by statisticians and probabilists. Knowledge of other metrics can provide a means of deriving bounds for another one in an applied problem. Considering other metrics can also provide alternate insights. We also give examples that show that rates of convergence can strongly depend on the metric chosen. Careful consideration is necessary when choosing a metric.

Robust Residuals And Diagnostics In Autoregressive Time Series, Kirk W. Anderson

Dissertations

One of the goals of model diagnostics is outlier detection. In particular, we would like to use the residuals, appropriately standardized, to “flag” outliers. Hopefully, our (robust) procedure has yielded a fit that resists undue influence by outlying points, while simultaneously drawing attention to these interesting points via residual analysis. In this study we consider several different methods of standardizing the residuals resulting from autoregression. A large sample approximation for the variance of rank-based first order autoregressive time series residuals is developed. This provides studentized residuals, specific to the time series model and estimation procedure. Simulation studies are presented that …

New Statitstical Methods For The Estimation Of The Mean And Standard Deviation From Normally Distributed Censored Samples, Abou El-Makarim Abd El-Alim Aboueissa

Dissertations

The main objective of this dissertation is to estimate the mean /x and standard deviation cr of a normal population from left-censored samples. We have developed new methods for calculating estimates for the mean and standard deviation of a normal population from left-censored samples. Some of these methods based on traditional estimating procedures. A new method of obtaining the Cohen maximum likelihood estimates for fx and cr without the aid of an auxiliary table will be introduced. This new method will be used to extend Cohen table of estimating the Cohen A-parameter that is required for calculating the maximum likelihood …

On Rank-Based Considerations For Generalized Linear Models And Generalized Estimating Equation Models, Diana R. Cucos

Dissertations

This study discusses rank-based robust methods for estimation of parameters and hypotheses testing in the generalized linear models (GLM) and generalized estimating equations (GEE) setting. The robust estimates are obtained by minimizing a Wilcoxon drop in dispersion function for linear or nonlinear regression models. In addition, diagnostic tools for outliers and influential observations are being developed. These models are generalizations of linear and nonlinear models. They allow for both nonlinear mean functions and heteroscedasticity of their random errors. This makes them quite useful in practice. Rank-based inference has been developed for linear models over the last thirty years. This inference …

Resolvability In Graphs, Varaporn Saenpholphat

Dissertations

The distance d (u, v ) between two vertices u and v in a connected graph G is the length of a shortest u - v path in G . For an ordered set W = { w1 , w2 , [Special characters omitted.] &cdots; , wk } of vertices in G and a vertex v of G , the code of v with respect to W is the k -vector cW (v ) = (d ( v, w1 ),d (v, w 2 ), [Special characters omitted.] &cdots; , d …

Multi-Level Decomposition Of Probabilistic Relations, Stanislaw Grygiel, Martin Zwick, Marek Perkowski

Complex Systems Faculty Publications and Presentations

Two methods of decomposition of probabilistic relations are presented in this paper. They consist of splitting relations (blocks) into pairs of smaller blocks related to each other by new variables generated in such a way so as to minimize a cost function which depends on the size and structure of the result. The decomposition is repeated iteratively until a stopping criterion is met. Topology and contents of the resulting structure develop dynamically in the decomposition process and reflect relationships hidden in the data.

Analysis Of Longitudinal Marginal Structural Models , Jennifer F. Bryan, Zhuo Yu, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In this article we construct and study estimators of the causal effect of a time-dependent treatment on survival in longitudinal studies. We employ a particular marginal structural model (MSM), and follow a general methodology for constructing estimating functions in censored data models. The inverse probability of treatment weighted (IPTW) estimator is used as an initial estimator and the corresponding treatment-orthogonalized, one-step estimator is consistent and asymptotically linear when the treatment mechanism is consistently estimated. We extend these methods to handle informative censoring. A simulation study demonstrates that the the treatment-orthogonalized, one-step estimator is superior to the IPTW estimator in terms …

On The Misuse Of Confidence Intervals For Two Means In Testing For The Significance Of The Difference Between The Means, George W. Ryan, Steven D. Leadbetter

Journal of Modern Applied Statistical Methods

Comparing individual confidence intervals of two population means is an incorrect procedure for determining the statistical significance of the difference between the means. We show conditions where confidence intervals for the means from two independent samples overlap and the difference between the means is in fact significant.

Constructive Criticism, Ronald C. Serlin

Journal of Modern Applied Statistical Methods

Attempts to attain knowledge as certified true belief have failed to circumvent Hume’s injunction against induction. Theories must be viewed as unprovable, improbable, and undisprovable. The empirical basis is fallible, and yet the method of conjectures and refutations is untouched by Hume’s insights. The implications for statistical methodology is that the requisite severity of testing is achieved through the use of robust procedures, whose assumptions have not been shown to be substantially violated, to test predesignated range null hypotheses. Nonparametric range null hypothesis tests need to be developed to examine whether or not effect sizes or measures of association, as …

Extensions Of The Concept Of Exchangeability And Their Applications, Phillip I. Good

Journal of Modern Applied Statistical Methods

Permutation tests provide exact p-values in a wide variety of practical testing situations. But permutation tests rely on the assumption of exchangeability, that is, under the hypothesis, the joint distribution of the observations is invariant under permutations of the subscripts. Observations are exchangeable if they are independent, identically distributed (i.i.d.), or if they are jointly normal with identical covariances. The range of applications of these exact, powerful, distribution-free tests can be enlarged through exchangeability- preserving transforms, asymptotic exchangeability, partial exchangeability, and weak exchangeability. Original exact tests for comparing the slopes of two regression lines and for the analysis of …

A Test Of Symmetry, Abdul R. Othman, H. J. Keselman, Rand R. Wilcox, Katherine Fradette, A. R. Padmanabhan

Journal of Modern Applied Statistical Methods

When data are nonnormal in form classical procedures for assessing treatment group equality are prone to distortions in rates of Type I error and power to detect effects. Replacing the usual means with trimmed means reduces rates of Type I error and increases sensitivity to detect effects. If data are skewed, say to the right, then it has been postulated that asymmetric trimming, to the right, should be better at controlling rates of Type I error and power to detect effects than symmetric trimming from both tails of the data distribution. Keselman, Wilcox, Othman and Fradette (2002) found that Babu, …

Best Regression Model Using Information Criteria, Phill Gagné, C. Mitchell Dayton

Journal of Modern Applied Statistical Methods

The accuracy of AIC and BIC is evaluated under simulated multiple regression conditions, varying number of total and valid predictors, R², and n. AIC and BIC were increasingly accurate as n increased and as total predictors decreased. Interactions of the ratio of valid/total predictors affected accuracy.

The Statistical Modeling Of The Fertility Of Chinese Women, Dudley L. Poston Jr.

Journal of Modern Applied Statistical Methods

This article is concerned with the statistical modeling of children ever born (CEB) fertility data. It is shown that in a low fertility population, such as China, the use of linear regression approaches to model CEB is statistically inappropriate because the distribution of the CEB variable is often heavily skewed with a long right tail. For five sub-groups of Chinese women, their fertility is modeled using Poisson, negative binomial, and ordinary least squares (OLS) regression models. It is shown that in almost all instances there would have been major errors of statistical inference had the interpretations of the results been …

Fermat, Schubert, Einstein, And Behrens-Fisher: The Probable Difference Between Two Means When Σ_1^2≠Σ_2^2, Shlomo S. Sawilowsky

Journal of Modern Applied Statistical Methods

The history of the Behrens-Fisher problem and some approximate solutions are reviewed. In outlining relevant statistical hypotheses on the probable difference between two means, the importance of the Behrens- Fisher problem from a theoretical perspective is acknowledged, but it is concluded that this problem is irrelevant for applied research in psychology, education, and related disciplines. The focus is better placed on “shift in location” and, more importantly, “shift in location and change in scale” treatment alternatives.

Double Median Ranked Set Sample: Comparing To Other Double Ranked Samples For Mean And Ratio Estimators, Hani M. Samawi, Eman M. Tawalbeh

Journal of Modern Applied Statistical Methods

Double median ranked set sample (DMRSS) and its properties for estimating the population mean, when the underlying distribution is assumed to be symmetric about its mean, are introduced. Also, the performance of DMRSS with respect to other ranked set samples and double ranked set samples, for estimating the population mean and ratio, is considered. Real data that consist of heights and diameters of 399 trees are used to illustrate the procedure. The analysis and simulation indicate that using DMRSS for estimating the population mean is more efficient than using the other ranked samples and double ranked samples schemes except in …

Robust Estimation Of Multivariate Failure Data With Time-Modulated Frailty, Pingfu Fu, J. Sunil Rao, Jiming Jiang

Journal of Modern Applied Statistical Methods

A time-modulated frailty model is proposed for analyzing multivariate failure data. The effect of frailties, which may not be constant over time, is discussed. We assume a parametric model for the baseline hazard, but avoid the parametric assumption for the frailty distribution. The well-known connection between survival times and Poisson regression model is used. The parameters of interest are estimated by generalized estimating equations (GEE) or by penalized GEE. Simulation studies show that the procedure is successful to detect the effect of time-modulated frailty. The method is also applied to a placebo controlled randomized clinical trial of gamma interferon, a …

Some Reflections On Significance Testing, Thomas R. Knapp

Journal of Modern Applied Statistical Methods

This essay presents a variation on a theme from my article “The use of tests of statistical significance”, which appeared in the Spring, 1999, issue of Mid-Western Educational Researcher.

Null Distribution Of The Likelihood Ratio Statistic For Feed-Forward Neural Networks, Douglas Landsittel, Harshinder Singh, Vincent C. Arena, Stewart J. Anderson

Journal of Modern Applied Statistical Methods

Despite recent publications exploring model complexity with modern regression methods, their dimensionality is rarely quantified in practice and the distributions of related test statistics are not well characterized. Through a simulation study, we describe the null distribution of the likelihood ratio statistic for several different feed-forward neural network models.

Combining Quantum Mechanical Calculations And A Χ^2 Fit In A Potential Energy Function For The Co_2 + O^+ Reaction, Ellen F. Sawilowsky

Journal of Modern Applied Statistical Methods

In order to compute a highly accurate statistical rate constant for the CO2 + O⁺ reaction, it is necessary to first calculate the potential energy of the system at many different geometric configurations. Quantum mechanical calculations are very time-consuming, making it difficult to obtain a sufficient number to allow for accurate interpolation. The number of quantum mechanical calculations required can be significantly reduced by using known relations in classical physics to calculate energy for configurations where the oxygen is relatively far from the CO2. A chi-squared fit to quantum mechanical points is obtained for these configurations, and the resulting …

Type I Error Rates For Rank-Based Tests Of Homogeneity Of Slopes, Alan J. Klockars, Tim P. Moses

Journal of Modern Applied Statistical Methods

The purpose of this study was to explicate two issues concerning the standard and rank based test of homogeneity of slopes. Two alternative ranking methods intended to address nonnormality and additive treatment effect patterns were developed and compared in terms of their ability to control Type I error. The results replicated previous findings of inflated Type I error rates with leptokurtic curves and with rank based tests with some patterns of additive treatment effects. The new nonparametric procedures generally control Type I error although they were slightly inflated with skewed distributions.

Exploration Of Distributions Of Ratio Of Partial Sum Of Sample Eigenvalues When All Population Eigenvalues Are The Same, Moonseong Heo

Journal of Modern Applied Statistical Methods

This paper explores empirically the first two moments of ratio of the partial sum of the first two sample eigenvalues to the sum of all eigenvalues when the population eigenvalues of a covariance matrix are all the same. Estimation of the first two moments can be practically crucial in assessing non-randomness of observed patterns on planar graphical displays based on lower rank approximations of data matrices. For derivation of the moments, exact and large sample asymptotic distributions of the sample ratios are reviewed but neither can be applicable to derivation of the moments. Therefore, I rely on simulations, where data …