Statistics and Probability Commons^™

A Comparison Of The D’Agostino S_U Test To The Triples Test For Testing Of Symmetry Versus Asymmetry As A Preliminary Test To Testing The Equality Of Means, Kimberly T. Perry, Michael R. Stoline

Journal of Modern Applied Statistical Methods

This paper evaluates the D’Agostino S_U test and the Triples test for testing symmetry versus asymmetry. These procedures are evaluated as preliminary tests in the selection of the most appropriate procedure for testing the equality of means with two independent samples under a variety of symmetric and asymmetric sampling situations. Key words: symmetry; asymmetry; preliminary testing.

Within Groups Multiple Comparisons Based On Robust Measures Of Location, Rand R. Wilcox, H. J. Keselman

Journal of Modern Applied Statistical Methods

Consider the problem of performing all pair-wise comparisons among J dependent groups based on measures of location associated with the marginal distributions. It is well known that the standard error of the sample mean can be large relative to other estimators when outliers are common. Two general strategies for addressing this problem are to trim a fixed proportion of observations or empirically check for outliers and remove (or down-weight) any that are found. However, simply applying conventional methods for means to the data that remain results in using the wrong standard error. Methods that address this problem have been proposed, …

Adaptive Tests For Ordered Categorical Data, Vance W. Berger, Anastasia Ivanova

Journal of Modern Applied Statistical Methods

Consider testing for independence against stochastic order in an ordered 2xJ contingency table, under product multinomial sampling. In applications one may wish to exploit prior information concerning the direction of the treatment effect, yet ultimately end up with a testing procedure with good frequentist properties. As such, a reasonable objective may be to simultaneously maximize power at a specified alternative and ensure reasonable power for all other alternatives of interest. For this objective, none of the available testing approaches are completely satisfactory. A new class of admissible adaptive tests is derived. Each test in this class strictly preserves the Type …

Accounting For Non-Independent Observations In 2×2 Tables, With Application To Correcting For Family Clustering In Exposure-Risk Relationship Studies, Leslie A. Kalsih, Katherine A. Riester, Stuart J. Pocock

Journal of Modern Applied Statistical Methods

Participants in epidemiologic studies may not represent statistically independent observations. We consider modifications to conventional analyses of 2×2 tables, including Fisher’s exact test and confidence intervals, to account for correlated observations in this setting. An example is provided, assessing the robustness of conclusions from a published analysis.

Simulation Study Of Chemical Inhibition Modeling, Pali Sen, Mary Anderson

Journal of Modern Applied Statistical Methods

The combined effects of the activities of different chemicals are of interest of this study. We simulate for the synthetic data, and fit experimental data for three models and estimate the parameters. We assess the fit of the synthetic data and the experimental data by comparing the coefficients of variation for the parameter estimates and identify the best model for the inhibition process.

On Distribution Function Estimation Using Double Ranked Set Samples With Application, Walid A. Abu-Dayyeh, Hani M. Samawi, Lara A. Bani-Hani

Journal of Modern Applied Statistical Methods

As a variation of ranked set sampling (RSS); double ranked set sampling (DRSS) was introduced by Al-Saleh and Al-Kadiri (2000), and it has been used only for estimating the mean of the population. In this paper DRSS will be used for estimating the distribution function (cdf). The efficiency of the proposed estimators will be obtained when ranking is perfect. Some inference on the distribution function will be drawn based on Kolomgrov-Smirnov statistic. It will be shown that using DRSS will increase the efficiency in this case.

On The Estimation Of Binomial Success Probability With Zero Occurrence In Sample, Mehdi Razzaghi

Journal of Modern Applied Statistical Methods

The problem of estimating the probability of a rare event when the sample shows no incidence of the event is considered. Several methodologies based on various statistical techniques are described and their relative performances are investigated. A decision theoretic approach for estimation of response probability when the sample contains zero responses is examined in depth. The properties of each method are discussed and an example from teratology is used to provide illustration and to demonstrate the results.

A Longitudinal Follow-Up Of Discrete Mass At Zero With Gap, Joseph L. Musial, Patrick D. Bridge, Nicol R. Shamey

Journal of Modern Applied Statistical Methods

The first part of this paper discusses a five-year systematic review of the Journal of Consulting and Clinical Psychology following the landmark power study conducted by Sawilowsky and Hillman (1992). The second part discusses a five-year longitudinal follow-up of a radically nonnormal population distribution: discrete mass at zero with gap. This distribution was based upon a real dataset.

Jmasm4: Critical Values For Four Nonparametric And/Or Distribution-Free Tests Of Location For Two Independent Samples, Bruce R. Fay

Journal of Modern Applied Statistical Methods

Researchers engaged in computer-intensive studies may need exact critical values, especially for sample sizes and alpha levels not normally found in published tables, as well as the ability to control ‘best-fit’ criteria. They may also benefit from the ability to directly generate these values rather than having to create lookup tables. Fortran 90 programs generate ‘best-conservative’ (bc) and ‘best-fit’ (bf) critical values with associated probabilities for the Kolmogorov-Smirnov test of general differences (bc), Rosenbaum’s test of location (bc), Tukey’s quick test (bc and bf)) and the Wilcoxon rank-sum test (bc).

Locally Efficient Estimation With Bivariate Right Censored Data , Christopher M. Quale, Mark J. Van Der Laan, James M. Robins

U.C. Berkeley Division of Biostatistics Working Paper Series

Estimation for bivariate right censored data is a problem that has had much study over the past 15 years. In this paper we propose a new class of estimators for the bivariate survivor function based on locally efficient estimation. The locally efficient estimator takes bivariate estimators Fn and Gn of the distributions of the time variables T1,T2 and the censoring variables C1,C2, respectively, and maps them to the resulting estimator. If Fn and Gn are consistent estimators of F and G, respectively, then the resulting estimator will be nonparametrically efficient (thus the term ``locally efficient''). However, if either Fn or …

An Empirical Study Of Marginal Structural Models For Time-Independent Treatment, Tanya A. Henneman, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In non-randomized treatment studies a significant problem for statisticians is determining how best to adjust for confounders. Marginal structural models (MSMs) and inverse probability of treatment weighted (IPTW) estimators are useful in analyzing the causal effect of treatment in observational studies. Given an IPTW estimator a doubly robust augmented IPTW (AIPTW) estimator orthogonalizes it resulting in a more e±cient estimator than the IPTW estimator. One purpose of this paper is to make a practical comparison between the IPTW estimator and the doubly robust AIPTW estimator via a series of Monte- Carlo simulations. We also consider the selection of the optimal …

Stochastic 2-D Navier-Stokes Equation, J. L. Menaldi, S. S. Sritharan

Mathematics Faculty Research Publications

In this paper we prove the existence and uniqueness of strong solutions for the stochastic Navier-Stokes equation in bounded and unbounded domains. These solutions are stochastic analogs of the classical Lions-Prodi solutions to the deterministic Navier-Stokes equation. Local monotonicity of the nonlinearity is exploited to obtain the solutions in a given probability space and this signi cantly improves the earlier techniques for obtaining strong solutions, which depended on pathwise solutions to the Navier-Stokes martingale problem where the probability space is also obtained as a part of the solution.

Student Fact Book, Fall 2002, Wright State University Lake Campus, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student fact book has general demographic information on all students enrolled at Wright State University Lake Campus for Fall Quarter, 2002.

Student Fact Book, Fall 2002, Twenty-Sixth Annual Edition, Wright State University, Office Of Student Information Systems, Wright State University

Wright State University Student Fact Books

The student fact book has general demographic information on all students enrolled at Wright State University for Fall Quarter, 2002.

The Kpss Test With Seasonal Dummies, Sainan Jin, Sainan Jin

Research Collection School Of Economics

It is shown that the KPSS test for stationarity may be applied without change to regressions with seasonal dummies. In particular, the limit distribution of the KPSS statistic is the same under both the null and alternative hypotheses whether or not seasonal dummies are used.

Support For Statistical Analysis Of The Configurable Port Simulation (Cports), Saurav Mazumdar

Electrical & Computer Engineering Theses & Dissertations

The primary objective of this thesis is to provide support for statistical analysis of CPortS: a transportation logistics simulation, which models the movement of military traffic through seaports and the interaction of the traffic with port infrastructure. By any standards, CPortS is a very large, data intensive simulation. It provides capabilities for analyzing many important issues such as port clearance and throughput. CPortS was classically run in single run mode. Only a single replication of the simulation was performed and conclusions were drawn from the results obtained. Users and analysts of CPortS performed multiple runs only to see the effect …

Numeric Issues In Test Software Correctness, Robert G. Hayes, Gary B. Hughes, Phillip M. Dorin, Raymond J. Toal

Statistics

Test system designers are comfortable with the concepts of precision and accuracy with regard to measurements achieved with modern instrumentation. In a well-designed test system, great care is taken to ensure accurate measurements, with rigorous attention to instrument specifications and calibration. However, measurement values are subjected to representation and manipulation as limited precision floating-point numbers by test software. This paper investigates some of the issues related to floating point representation of measurement values, as well as the consequences of algorithm selection. To illustrate, we consider the test case of standard deviation calculations as used in the testing of infrared focal …

The Analysis Of Placement Values For Evaluating Discriminatory Measures, Margaret S. Pepe, Tianxi Cai

UW Biostatistics Working Paper Series

The idea of using measurements such as biomarkers, clinical data, or molecular biology assays for classification and prediction is popular in modern medicine. The scientific evaluation of such measures includes assessing the accuracy with which they predict the outcome of interest. Receiver operating characteristic curves are commonly used for evaluating the accuracy of diagnostic tests. They can be applied more broadly, indeed to any problem involving classification to two states or populations (D = 0 or D = 1). We show that the ROC curve can be interpreted as a cumulative distribution function for the discriminatory measure Y in the …

Accelerated Hazards Model: Method, Theory And Applications, Ying Qing Chen, Nicholas P. Jewell, Jingrong Yang

U.C. Berkeley Division of Biostatistics Working Paper Series

In an accelerated hazards model, the hazard functions of a failure time are related through the time scale-change, which is often a function of covariates and associated parameters. When the hazard functions have special properties, such as monotonicity in time, the parameters may be clinically meaningful in measuring a treatment effect. This paper reviews methodological and theoretical development of this model. Applications of the accelerated hazards model including sample size calculation in clinical trials, are also explored.

Locally Efficient Estimation Of Regression Parameters Using Current Status Data, Chris Andrews, Mark J. Van Der Laan, James M. Robins

U.C. Berkeley Division of Biostatistics Working Paper Series

In biostatistics applications interest often focuses on the estimation of the distribution of a time-variable T. If one only observes whether or not T exceeds an observed monitoring time C, then the data structure is called current status data, also known as interval censored data, case I. We consider this data structure extended to allow the presence of both time-independent covariates and time-dependent covariate processes that are observed until the monitoring time. We assume that the monitoring process satisfies coarsening at random.

Our goal is to estimate the regression parameter beta of the regression model T = Z*beta+epsilon where the …

Case-Control Current Status Data, Nicholas P. Jewell, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Current status observation on survival times has recently been widely studied. An extreme form of interval censoring, this data structure refers to situations where the only available information on a survival random variable, T, is whether or not T exceeds a random independent monitoring time C, a binary random variable, Y. To date, nonparametric analyses of current status data have assumed the availability of i.i.d. random samples of the random variable (Y, C), or a similar random sample at each of a set of fixed monitoring times. In many situations, it is useful to consider a case-control sampling scheme. Here, …

Why Prefer Double Robust Estimates? Illustration With Causal Point Treatment Studies, Romain Neugebauer, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

In point treatment marginal structural models with treatment A, outcome Y and covariates W, causal parameters can be estimated under the assumption of no unobserved confounders. Three estimates can be used: the G-computation, Inverse Probability of Treatment Weighted (IPTW) or Double Robust (DR) estimates. The properties of the IPTW and DR estimates are known under an assumption on the treatment mechanism that we name "Experimental Treatment Assignment" (ETA) assumption. We show that the DR estimating function is unbiased when the ETA assumption is violated if the model used to regress Y on A and W is correctly specified. The practical …

Bivariate Current Status Data, Mark J. Van Der Laan, Nicholas P. Jewell

U.C. Berkeley Division of Biostatistics Working Paper Series

In many applications, it is often of interest to estimate a bivariate distribution of two survival random variables. Complete observation of such random variables is often incomplete. If one only observes whether or not each of the individual survival times exceeds a common observed monitoring time C, then the data structure is referred to as bivariate current status data (Wang and Ding, 2000). For such data, we show that the identifiable part of the joint distribution is represented by three univariate cumulative distribution functions, namely the two marginal cumulative distribution functions, and the bivariate cumulative distribution function evaluated on the …

Current Status Data: Review, Recent Developments And Open Problems, Nicholas P. Jewell, Mark J. Van Der Laan

U.C. Berkeley Division of Biostatistics Working Paper Series

Researchers working with survival data are by now adept at handling issues associated with incomplete data, particular those associated with various forms of censoring. An extreme form of interval censoring, known as current status observation, refers to situations where the only available information on a survival random variable T is whether or not T exceeds a random independent monitoring time C. This article contains a brief review of the extensive literature on the analysis of current status data, discussing the implications of response-based sampling on these methods. The majority of the paper introduces some recent extensions of these ideas to …

Matroid Duality From Topological Duality In Surfaces Of Nonnegative Euler Characteristic, Dan Slilaty

Mathematics and Statistics Faculty Publications

Let G be a connected graph that is 2-cell embedded in a surface S, and let G* be its topological dual graph. We will define and discuss several matroids whose element set is E(G), for S homeomorphic to the plane, projective plane, or torus. We will also state and prove old and new results of the type that the dual matroid of G is the matroid of the topological dual G*.

Statistical Image Analysis Of Spotted Arrays, Filippo Posta

Theses

There is a lot of systematic and specific variability in microarray experiments, this variability affects measured gene expression levels, leading to unreliable gene profiling or an heavy load of extra experiment to statistically confirm the data observed in one experiment.

The aim of this work is to systematically analyze, using statistics, the image derived from a cDNA microarray experiment to have a better understanding of this variability and thus a better confidence over the data obtained from an experiment.

Using technologies available at the Center for Applied Genomics, Newark, New Jersey. Selected images derived from different type of microarray experiments …

An Algorithm For Estimating The Quality Of Microarrays, Ajeet S. Sodhi

Theses

Microarray technology is currently one of the most valuable gene expression tools in molecular biology allowing the experimenter to simultaneously quantify the expression of thousands of genes. It is also one of the most difficult tools to use accurately as each microarray produces a large amount of information that needs to be inspected and normalized before analysis. As the size of a microarray or number of replicates increase, the use of manual inspection becomes impractical. The aim of this thesis is to introduce an algorithm that evaluates each feature of a microarray from the scanned data file. A quality score …

Semiparametric Regression Analysis On Longitudinal Pattern Of Recurrent Gap Times, Ying Qing Chen, Mei-Cheng Wang, Yijian Huang

U.C. Berkeley Division of Biostatistics Working Paper Series

In longitudinal studies, individual subjects may experience recurrent events of the same type over a relatively long period of time. The longitudinal pattern of the gaps between the successive recurrent events is often of great research interest. In this article, the probability structure of the recurrent gap times is first explored in the presence of censoring. According to the discovered structure, we introduce the proportional reverse-time hazards models with unspecified baseline functions to accommodate heterogeneous individual underlying distributions, when the ongitudinal pattern parameter is of main interest. Inference procedures are proposed and studied by way of proper riskset construction. The …

Multiple Hypothesis Testing In Microarray Experiments, Sandrine Dudoit, Juliet Popper Shaffer, Jennifer C. Boldrick

U.C. Berkeley Division of Biostatistics Working Paper Series

DNA microarrays are a new and promising biotechnology which allows the monitoring of expression levels in cells for thousands of genes simultaneously. An important and common question in microarray experiments is the identification of differentially expressed genes, i.e., genes whose expression levels are associated with a response or covariate of interest. The biological question of differential expression can be restated as a problem in multiple hypothesis testing: the simultaneous test for each gene of the null hypothesis of no association between the expression levels and the responses or covariates. As a typical microarray experiment measures expression levels for thousands of …

Estimation Of The Bivariate Survival Function With Generalized Bivariate Right Censored Data Structures, Sunduz Keles, Mark J. Van Der Laan, James M. Robins

U.C. Berkeley Division of Biostatistics Working Paper Series

We propose a bivariate survival function estimator for a general right censored data structure that includes a time dependent covariate process. Firstly, an initial estimator that generalizes Dabrowska's (1988) estimator is introduced. We obtain this estimator by a general methodology of constructing estimating functions in censored data models. The initial estimator is guaranteed to improve on Dabrowska's estimator and remains consistent and asymptotically linear under informative censoring schemes if the censoring mechanism is estimated consistently. We then construct an orthogonalized estimating function which results in a more robust and efficient estimator than our initial estimator. A simulation study demonstrates the …