We revisit the problem of interval estimation of a binomial proportion. The erratic behavior of the coverage probability of the standard Wald confidence interval has previously been remarked on in the literature (Blyth and Still, Agresti and Coull, Santner and others). We begin by showing that the chaotic coverage properties of the Wald interval are far more persistent than is appreciated. Furthermore, common textbook prescriptions regarding its safety are misleading and defective in several respects and cannot be trusted.

This leads us to consideration of alternative intervals. A number of natural alternatives are presented, each with its motivation and context. Each interval is examined for its coverage probability and its length. Based on this analysis, we recommend the Wilson interval or the equal-tailed Jeffreys prior interval for small n and the interval suggested in Agresti and Coull for larger n. We also provide an additional frequentist justification for use of the Jeffreys interval.

Nonparametric regression techniques are often sensitive to the presence of correlation in the errors. The practical consequences of this sensitivity are explained, including the breakdown of several popular data-driven smoothing parameter selection methods. We review the existing literature in kernel regression, smoothing splines and wavelet regression under correlation, both for short-range and long-range dependence. Extensions to random design, higher dimensional models and adaptive estimation are discussed.

At the early stage of drug discovery, many thousands of chemical compounds can be synthesized and tested (assayed) for potency (activity) with high throughput screening (HTS). With ever-increasing numbers of compounds to be tested (now often in the neighborhood of 500,000) it remains a challenge to find strategies via sequential design that reduce costs while locating classes of active compounds. Initial screening of a modest number of selected compounds (first-stage) is used to construct a structure-activity relationship (SAR). Based on this model, a second-stage sample is selected, the SAR updated and, if no more sampling is done, the activities of not yet tested compounds are predicted. Instead of stopping, the SAR could be used to determine another stage of sampling after which the SAR is updated and the process repeated.

We use existing data on the potency and chemical structure of 70,223 compounds to investigate various sequential testing schemes. Evidence on two assays supports the conclusion that a rather small number of samples selected according to the proposed scheme can more than triple the rate at which active compounds are identified and also produce SARs effective for identifying chemical structure. A different set of 52,883 compounds is used to confirm our findings.

One surprising conclusion of the study is that the design of the initial sample stage may be unimportant: random selection or systematic methods based on chemical structures are equally effective.

On November 15, 2000 the statistics community was saddened by the death of one of its most prominent members and leaders, Oscar Kempthorne, who had given over 50 years of his life to statistical science as an educator and researcher. Obituaries and other accounts detailing aspects of and achievements during his personal and professional life have appeared elsewhere (IMS Bulletin 30 (2), 2001; Bancroft, 1984; David, 1984). The purpose of this paper is different: it is to highlight his major contributions to statistical science, and to indicate how these ideas are still guiding statistical thinking today.

Oscar Kempthorne contributedlargely to three major areas: to experimental design, to genetic statistics, and to the philosophy and foundations of statistics. These seem to be rather distinct areas, but his research shows a common thread in the form of his concern for acquiring scientifically sound data and interpreting such data. In this context he considered the analysis of variance as one of the most powerful statistical techniques, and it is therefore not surprising that much of his research, certainly in experimental design and genetic statistics, centers around this technique. This work established him very early on as one of the leading statisticians of our time.

Leo Breiman was born in New York City on January 27, 1928. His parents and he migrated five years later to San Francisco where he began school. During Leo's junior high school years, his family moved again, to Los Angeles. Leo graduated from Roosevelt High School in 1945 and entered the California Institute of Technology, from which he graduated four years later with a major in physics. He earned his Master's Degree in mathematics at Columbia University in 1950 and his Ph.D. in Mathematics at the University of California, Berkeley in 1954. Leo has broad ranging scientific and mathematical interests, including information theory and the theory of gambling. He has been involved in applications coming from studies of automobile traffic, air quality and toxic substance recognition. He is the author of a celebrated graduate text on probability theory, is one of four authors of Classification and Regression Trees and its associated CART^R software and has also written two other books. With Jerome Friedman, Leo developed the ACE (alternating conditional expectations) algorithm by which nonlinear relationships between the dependent variable and predictor variables in regression are described. He is the originator of “bagging” and “arcing,” both computer­intensive approaches to classification that are of much current interest.

Leo's professional positions have included being on the faculty of the Department of Mathematics at UCLA, an independent consultant for 13 years and Professor of Statistics and founding Director of the Statistical Computing Facility at the University of California, Berkeley. In addition, he has had visiting positions at Stanford and at Yale. For his many contributions, Leo has been honored by Fellowship in the Institute of Mathematical Statistics and in the American Statistical Association. He is an elected member of the American Academy of Arts and Sciences and received the Berkeley Citation from the University of California. The interests and accomplishments of Leo Breiman extend outside the areas of professional statistician and probabilist. He was a waiter in the Catskills, a dishwasher in the Merchant Marine, a trekker into the heart of rainforest Africa, an active father to many children from a small agrarian Mexican village, a member and President of the Santa Monica School Board, the architect of his stunning home and an accomplished sculptor. Leo and his wife, Mary Lou, reside in Berkeley. He is the father of two daughters, Rebecca and Jessica.