We analyze tests for long-run abnormal returns and document that two approaches yield well-specified test statistics in random samples. The first uses a traditional event study framework and buy-and-hold abnormal returns calculated using carefully constructed reference portfolios. Inference is based on either a skewnessadjusted t-statistic or the empirically generated distribution of long-run abnormal returns. The second approach is based on calculation of mean monthly abnormal returns using calendar-time portfolios and a time-series t-statistic. Though both approaches perform well in random samples, misspecification in nonrandom samples is pervasive. Thus, analysis of long-run abnormal returns is treacherous. COMMONLY USED METHODS TO TEST for long-run abnormal stock returns yield misspecified test statistics, as documented by Barber and Lyon ~1997a! and Kothari and Warner ~1997!. 1 Simulations reveal that empirical rejection levels routinely exceed theoretical rejection levels in these tests. In combination, these papers highlight three causes for this misspecification. First, the

This report addresses the characterization of measurements that include epistemic uncertainties in the form of intervals. It reviews the application of basic descriptive statistics to data sets which contain intervals rather than exclusively point estimates. It describes algorithms to compute various means, the median and other percentiles, variance, interquartile range, moments, confidence limits, and other important statistics and summarizes the computability of these statistics as a function of sample size and characteristics of the intervals in the data (degree of overlap, size and regularity of widths, etc.). It also reviews the prospects for analyzing such data sets with the methods of inferential statistics such as outlier detection and regressions. The report explores the tradeoff between measurement precision and sample size in statistical results that are sensitive to both. It also argues that an approach based on interval statistics could be a reasonable alternative to current standard methods for evaluating, expressing and propagating measurement uncertainties.

We discuss Skart, an automated batch-means procedure for constructing a skewness- and autoregression-adjusted confidence interval (CI) for the steady-state mean of a simulation output process in either discrete time (i.e., observation-based statistics) or continuous time (i.e., time-persistent statistics). Skart is a sequential procedure designed to deliver a CI that satisfies user-specified requirements concerning not only the CI’s coverage probability but also the absolute or relative precision provided by its half-length. Skart exploits separate adjustments to the half-length of the classical batch-means CI so as to account for the effects on the distribution of the underlying Student’st-statistic that arise from skewness (nonnormality) and autocorrelation of the batch means. The skewness adjustment is based on a modified Cornish-Fisher expansion for the classical batch-means Student’st-ratio, and the autocorrelation adjustment is based on an autoregressive approximation to the batch-means process for sufficiently large batch sizes. Skart also delivers a point estimator for the steady-state mean that is approximately free of initialization bias. The duration of the associated warm-up period (i.e., the statistics clearing time) is based on iteratively applying von Neumann’s randomness test to spaced batch means with progressively increasing batch sizes and interbatch spacer sizes. In an experimental performance evaluation involving a wide range of test processes, Skart compared favorably with other simulation analysis

Let X1,..., Xn be i.i.d. random variables with known variance and skewness. A one-sided confidence interval for the mean with approximate confidence level α can be constructed using normal approximation. For skew distributions the actual confidence level will then be α+o(1). We propose a method for obtaining confidence intervals with confidence level α+o(n −1/2) using skewness correcting pseudo-random variables. The method is compared with a known method; Edgeworth correction. h h Acknowledgements I would like to thank my advisor Silvelyn Zwanzig for introducing me to the subject, for mathematical and stylistic guidance and for always encouraging me. I would also like to thank my friends and teachers at and around the department of mathematics for having inspired me to study mathematics, and for continuing to inspire me. 3 h

The objective is this investigation is to better understand the relationship between cancer and environmental pollutants. From the National Cancer Institute (NCI), we chose the cancer mortality data that is available on their Internet site as the Cancer Atlas. For environmental pollutant information, we chose to focus on a database that is also widely used and accessible: the Toxic Release Inventory (TRI) available on the internet as TRI Explorer. This ecological study initially explored derived environmental statistics from counties in Northeast Ohio with high rates of childhood leukemia over more than 40 years and from toxic release data spanning more than a decade. Exploratory data analysis suggests that higher releases of chemicals in the past are associated with observed higher cancer mortality. Additional regions explored include all counties of all states with high cancer mortality rates and/or large air emissions of cancer causing chemicals. Further analysis comparing and ranking all states does not add to the association. The strengths and limitations of an ecological study will be discussed. The integration of health and environmental data is in its infancy. The

This paper develops new methodology, together with related theories, for combining information from independent studies through confidence distributions. A formal definition of a confidence distribution and its asymptotic counterpart (i.e., asymptotic confidence distribution) are given and illustrated in the context of combining information. Two general combination methods are developed: the first along the lines of combining p-values, with some notable differences in regard to optimality of Bahadur type efficiency; the second by multiplying and normalizing confidence densities. The latter approach is inspired by the common approach of multiplying likelihood functions for combining parametric information. The paper also develops adaptive combining methods, with supporting asymptotic theory which should be of practical interest. The key point of the adaptive development is that the methods attempt to combine only the correct information, downweighting or excluding studies containing little or wrong information about the true parameter of interest. The combination methodologies are illustrated in simulated and real data examples with a variety of applications. 1. Introduction and motivations

Abstract: The notion of confidence distribution (CD), an entirely frequentist concept, is in essence a Neymanian interpretation of Fisher’s Fiducial distribution. It contains information related to every kind of frequentist inference. In this article, a CD is viewed as a distribution estimator of a parameter. This leads naturally to consideration of the information contained in CD, comparison of CDs and optimal CDs, and connection of the CD concept to the (profile) likelihood function. A formal development of a multiparameter CD is also presented. 1. Introduction and