We present a statistical perspective on boosting. Special emphasis is given to estimating potentially complex parametric or nonparametric models, including generalized linear and additive models as well as regression models for survival analysis. Concepts of degrees of freedom and corresponding Akaike or Bayesian information criteria, particularly useful for regularization and variable selection in high-dimensional covariate spaces, are discussed as well.

The practical aspects of boosting procedures for fitting statistical models are illustrated by means of the dedicated open-source software package mboost. This package implements functions which can be used for model fitting, prediction and variable selection. It is flexible, allowing for the implementation of new boosting algorithms optimizing user-specified loss functions.

The authors are doing the readers of Statistical Science a true service with a well-written and up-to-date overview of boosting that originated with the seminal algorithms of Freund and Schapire. Equally, we are grateful for high-level software that will permit a larger readership to experiment with, or simply apply, boosting-inspired model fitting. The authors show us a world of methodology that illustrates how a fundamental innovation can penetrate every nook and cranny of statistical thinking and practice. They introduce the reader to one particular interpretation of boosting and then give a display of its potential with extensions from classification (where it all started) to least squares, exponential family models, survival analysis, to base-learners other than trees such as smoothing splines, to degrees of freedom and regularization, and to fascinating recent work in model selection. The uninitiated reader will find that the authors did a nice job of presenting a certain coherent and useful interpretation of boosting. The other reader, though, who has watched the business of boosting for a while, may have quibbles with the authors over details of the historic record and, more importantly, over their optimism about the current state of theoretical knowledge. In fact, as much as “the statistical view” has proven fruitful, it has also resulted in some ideas about why boosting works that may be misconceived, and in some recommendations that may be misguided.

When outcomes are missing for reasons beyond an investigator’s control, there are two different ways to adjust a parameter estimate for covariates that may be related both to the outcome and to missingness. One approach is to model the relationships between the covariates and the outcome and use those relationships to predict the missing values. Another is to model the probabilities of missingness given the covariates and incorporate them into a weighted or stratified estimate. Doubly robust (DR) procedures apply both types of model simultaneously and produce a consistent estimate of the parameter if either of the two models has been correctly specified. In this article, we show that DR estimates can be constructed in many ways. We compare the performance of various DR and non-DR estimates of a population mean in a simulated example where both models are incorrect but neither is grossly misspecified. Methods that use inverse-probabilities as weights, whether they are DR or not, are sensitive to misspecification of the propensity model when some estimated propensities are small. Many DR methods perform better than simple inverse-probability weighting. None of the DR methods we tried, however, improved upon the performance of simple regression-based prediction of the missing values. This study does not represent every missing-data problem that will arise in practice. But it does demonstrate that, in at least some settings, two wrong models are not better than one.

A traffic performance measurement system, PeMS, currently functions as a statewide repository for traffic data gathered by thousands of automatic sensors. It has integrated data collection, processing and communications infrastructure with data storage and analytical tools. In this paper, we discuss statistical issues that have emerged as we attempt to process a data stream of 2 GB per day of wildly varying quality. In particular, we focus on detecting sensor malfunction, imputation of missing or bad data, estimation of velocity and forecasting of travel times on freeway networks.

At a superficial level, the idea of maximum likelihood must be prehistoric: early hunters and gatherers may not have used the words “method of maximum likelihood” to describe their choice of where and how to hunt and gather, but it is hard to believe they would have been surprised if their method had been described in those terms. It seems a simple, even unassailable idea: Who would rise to argue in favor of a method of minimum likelihood, or even mediocre likelihood? And yet the mathematical history of the topic shows this “simple idea” is really anything but simple. Joseph Louis Lagrange, Daniel Bernoulli, Leonard Euler, Pierre Simon Laplace and Carl Friedrich Gauss are only some of those who explored the topic, not always in ways we would sanction today. In this article, that history is reviewed from back well before Fisher to the time of Lucien Le Cam’s dissertation. In the process Fisher’s unpublished 1930 characterization of conditions for the consistency and efficiency of maximum likelihood estimates is presented, and the mathematical basis of his three proofs discussed. In particular, Fisher’s derivation of the information inequality is seen to be derived from his work on the analysis of variance, and his later approach via estimating functions was derived from Euler’s Relation for homogeneous functions. The reaction to Fisher’s work is reviewed, and some lessons drawn.

Seymour Geisser received his bachelor’s degree in Mathematics from the City College of New York in 1950, and his M.A. and Ph.D. degrees in Mathematical Statistics at the University of North Carolina in 1952 and 1955, respectively. He then held positions at the National Bureau of Standards and the National Institute of Mental Health until 1961. From 1961 until 1965, he was Chief of the Biometry Section at the National Institute of Arthritis and Metabolic Diseases, and also held the position of Professorial Lecturer at the George Washington University from 1960 to 1965. From 1965 to 1970, he was the founding Chair of the Department of Statistics at the State University of New York, Buffalo, and in 1971, he became the founding Director of the School of Statistics at the University of Minnesota, remaining in that position until 2001. He held visiting professorships at Iowa State University, 1960; University of Wisconsin, 1964; University of Tel-Aviv (Israel), 1971; University of Waterloo (Canada), 1972; Stanford University, 1976, 1977, 1988; Carnegie Mellon University, 1976; University of the Orange Free State (South Africa), 1978, 1993; Harvard University, 1981; University of Chicago, 1985; University of Warwick (England), 1986; University of Modena (Italy), 1996; and National Chiao Tung University (Taiwan), 1998. He was the Lady Davis Visiting Professor, Hebrew University of Jerusalem, 1991, 1994, 1999, and the Schor Scholar, Merck Research Laboratories, 2002-2003. He was a Fellow of the Institute of Mathematical Statistics and the American Statistical Association.

Seymour is listed in World Men of Science, American Men and Women of Science and Who’s Who in America. He served on numerous committees for the National Institutes of Health, Food and Drug Administration, National Institute of Statistical Science and National Research Council. In addition, he was a National Science Foundation Lecturer in Statistics from 1966–1969; member of the National Research Council Committee on National Statistics from 1984–1987; Chair of the National Academy of Sciences panel on Occupational Safety and Health Statistics from 1986–1987; and he served on Program Review Committees for many universities. He delivered the American Statistical Association President’s Invited Address in 1991.

Seymour authored or coauthored 176 scientific articles, discussions, book reviews and books over his career. One of his articles, “On methods in the analysis of profile data,” which was coauthored by S. W. Greenhouse, and published in Psychometrika in 1959, is listed as a citation classic. He pioneered several important areas of statistical endeavor. He and Mervyn Stone simultaneously and independently invented the now popular statistical method called “cross-validation,” which is used for validating statistical models. Dr. Geisser’s paper on the subject, “The predictive sample reuse method with applications,” was published in the Journal of the American Statistical Association in 1975. He pioneered the areas of Bayesian multivariate analysis and discrimination, Bayesian diagnostics for statistical prediction and estimation models, Bayesian interim analysis, testing for Hardy–Weinberg equilibrium using forensic DNA data, and the optimal administration of multiple diagnostic screening tests.

Seymour was primarily noted for his sustained focus on prediction in Statistics. This began with his work on Bayesian classification. He gave an early exposition in his article, “The inferential use of predictive distributions,” published in Foundations of Statistical Inference in 1971. Most of his work in this area is summarized in his monograph, Predictive Inference: An Introduction published by Chapman and Hall in 1993. The essence of his argument was that Statistics should focus on observable quantities rather than on unobservable parameters that often do not exist and have been incorporated largely for convenience. He argued that the success of a statistical model should be measured by the quality of the predictions made from it. He pointed out that interest in model parameters often seemed to be based more on interest in ease of mathematical display than in their scientific utility.

Shortly after it was introduced, he gave his attention to forensic DNA profiling. He was involved as an expert witness in 100 litigations involving murder, rape, paternity, and other issues. His experiences in dealing with the FBI throughout these litigations are catalogued in his paper, “Statistics, litigation and conduct unbecoming,” published in Statistical Science in the Courtroom in 2000. His primary purpose in these litigations was to point out that statistical calculations displayed in court should be valid. It was his contention that the statistical methods then being used by the prosecution in DNA cases were flawed.

Finally, he was proud of his role in the development of the University of Minnesota School of Statistics and its graduate program. During his tenure there, he was responsible for hiring outstanding faculty who have since become leaders in their areas of expertise. Moreover, many of the students obtaining their Ph.D. degrees at the University of Minnesota have also become prominent in their respective fields. Seymour was substantially responsible for creating an educational environment that valued the foundations of Statistics beyond mere technical expertise.

Two special conferences were convened to honor the contributions of Seymour to the field of Statistics. The first was organized by Jack Lee and held at the National Chiao Tung University of Taiwan in December of 1995. The second was organized by Glen Meeden and held at the University of Minnesota in May of 2002. In conjunction with the former conference, a special volume entitled, Modeling and Prediction: Honoring Seymour Geisser, was published in 1996.

Most recently, Seymour compiled his lecture notes into a manuscript entitled, Modes of Parametric Statistical Inference [published by Wiley in 2006]. The book provides a broad view of the foundations of Statistics and invites discussion of the relative merits of different modes of statistical inference, method, and thought. His life’s work exemplifies the presentation of thoughtful, principled, reasoned, and coherent statistical methods to be used in the search for scientific truth.

Seymour Geisser died March 11, 2004.

The Department of Statistics at the University of Minnesota has established the Seymour Geisser Lectureship in Statistics. Each year, starting in the Fall of 2005, an individual will be named the Seymour Geisser Lecturer for that year and will be invited to give a special lecture. Individuals will be selected on the basis of excellence in statistical endeavors and their corresponding contributions to science, both statistical and otherwise. For more information or to see his curriculum vitae, visit the University of Minnesota, Department of Statistics web page, www.stat.umn.edu.

Born January 11, 1921 in New York City, Monroe Sirken grew up in a suburb of Pasadena, California. He earned B.A. and M.A. degrees in sociology at UCLA in 1946 and 1947, and a Ph.D. in 1950 in sociology with a minor in mathematics at the University of Washington in 1950 where Professor Z. W. Birnbaum was his mentor and thesis advisor. As a Post-Doctoral Fellow of the Social Science Research Council, Monroe spent 1950–1951 at the Statistics Laboratory, University of California at Berkeley and the Office of the Assistant Director for Research, U.S. Bureau of the Census in Suitland, Maryland.

Monroe visited the Census Bureau at a time of great change in the use of sampling and survey methods, and decided to remain. He began his government career there in 1951 as a mathematical statistician, and moved to the National Office of Vital Statistics (NOVS) in 1953 where he was an actuarial mathematician and a mathematical statistician. He has held a variety of research and administrative positions at the National Center for Health Statistics (NCHS) and he was the Associate Director, Research and Methodology and the Director, Office of Research and Methodology until 1996 when he became a senior research scientist, the title he currently holds.

Aside from administrative responsibilities, Monroe’s major professional interests have been conducting and fostering survey and statistical research responsive to the needs of federal statistics. His interest in the design of rare and sensitive population surveys led to the development of network sampling which improves precision by linking multiple selection units to the same observation units. His interest in fostering research on the cognitive aspects of survey methods led to the establishment of permanent questionnaire design research laboratories, first at NCHS and later at other federal statistical agencies here and abroad.

Monroe has been active in serving the statistical community. He has served on many committees of the American Statistical Association (ASA) and the Washington Statistical Society (WSS). He is a charter member of the Federal Committee on Statistical Methodology (FCSM) and chairs its research subcommittee that oversees a grants program in statistical and survey research that is funded by a consortium of federal statistical agencies, and administered by the National Science Foundation. He is a Fellow of the American Statistical Association and the American Association for the Advancement of Science, and is an elected member of the International Statistical Institute. He is the recipient of the Public Health Service Superior Service Award, and the ASA WSS Roger Herriot Award for Innovation in Government Statistics.