Stephen E. Fienberg

Graphical Methods in Statistics

Abstract Graphical methods have played a central role in the development of statistical theory and practice. This presentation briefly reviews some of the highlights in the historical development of statistical graphics and gives a simple taxonomy that can be used to characterize the current use of graphical methods. This taxonomy is used to describe the evolution of the use of graphics in some major statistical and related scientific journals. Some recent advances in the use of graphical methods for statistical analysis are reviewed, and several graphical methods for the statistical presentation of data are illustrated, including the use of multicolor maps.

Simultaneous Estimation of Multinomial Cell Probabilities

Abstract A new estimator, p*, of the multinomial parameter vector is proposed, and it is shown to be a better choice in most situations than the usual estimator, (the vector of observed proportions). The risk functions (expected squared-error loss) of these two estimators are examined in three ways using: (a) exact calculations, (b) standard asymptotic theory, and (c) a novel asymptotic framework in which the number of cells is large and the number of observations per cell is moderate. The general superiority of p* over in large sparse multinomials is thus revealed. The novel asymptotic framework may also provide insight in other multinomial problems.

Recent Econometric Modeling of Crime and Punishment Support for the Deterrence Hypothesis

In this article we review some recent attempts to develop econometric models for assessing the deterrent effect of punishment on crime, as well as analyses carried out to validate these models. The formulation of the basic econometric model considered here is due to Becker, and the detailed specification of the model, along with much of the empirical work reviewed, has been carried out by Ehrlich. We find serious flaws with the Becker- Ehrlich model, with the data used in its empirical implementation, and with Ehrlichs conclusions regarding evidence to support the deterrent effect of punishment on crime. Indeed, we can find no reliable empirical support in the existing economics literature either for or against the deterrence hypothesis.

Estimating the Total Overstatement Error in Accounting Populations

Abstract Auditors wishing to estimate the total amount of errors in a set of accounts have tended to use estimation procedures which rely on approximate normality for large sample sizes. Since this reliance is often not well-founded for sample sizes used in auditing practice, efforts have been made to circumvent this difficulty. This paper will briefly describe these efforts and then present a new approach based on the multinomial probability distribution which yields confidence bounds with known confidence levels for all sample sizes.

A Framework for the Development of Measurement Instruments for Evaluating the Introductory Statistics Course

Abstract This paper proposes a framework for the development of instruments to measure content learning and problem-solving skills for the introductory statistics course. This framework is based upon a model of the problem-solving process central to statistical reasoning. The framework defines and interrelates six measurement tasks: (1) subjective reports; (2) reports concerning truth, falsity, or equivalence; (3) supply the appropriate missing information in a message; (4) answer a question based upon a specific message; (S) reproduce a message; and (6) carry out a procedure.

On small world statistics

Thesmall-world problem revolves around the tracing of a line of acquaintances linking any two persons chosen at random. This paper discusses the statistical analysis of data arising out of two experimental studies of the small-world problem. The estimation of parameters in two previously proposed models is discussed, and the goodness-of-fit of these models is considered.