Many practical studies rely on hypothesis testing procedures applied to data sets with missing information. An important part of the analysis is to determine the impact of the missing data on the performance of the test, and this can be done by properly quantifying the relative (to complete data) amount of available information. The problem is directly motivated by applications to studies, such as linkage analyses and haplotype-based association projects, designed to identify genetic contributions to complex diseases. In the genetic studies the relative information measures are needed for the experimental design, technology comparison, interpretation of the data, and for understanding the behavior of some of the inference tools. The central difficulties in constructing such information measures arise from the multiple, and sometimes conflicting, aims in practice. For large samples, we show that a satisfactory, likelihood-based general solution exists by using appropriate forms of the relative Kullback–Leibler information, and that the proposed measures are computationally inexpensive given the maximized likelihoods with the observed data. Two measures are introduced, under the null and alternative hypothesis respectively. We exemplify the measures on data coming from mapping studies on the inflammatory bowel disease and diabetes. For small-sample problems, which appear rather frequently in practice and sometimes in disguised forms (e.g., measuring individual contributions to a large study), the robust Bayesian approach holds great promise, though the choice of a general-purpose “default prior” is a very challenging problem. We also report several intriguing connections encountered in our investigation, such as the connection with the fundamental identity for the EM algorithm, the connection with the second CR (Chapman–Robbins) lower information bound, the connection with entropy, and connections between likelihood ratios and Bayes factors. We hope that these seemingly unrelated connections, as well as our specific proposals, will stimulate a general discussion and research in this theoretically fascinating and practically needed area.

Bayesian model comparison requires the specification of a prior distribution on the parameter space of each candidate model. In this connection two concerns arise: on the one hand the elicitation task rapidly becomes prohibitive as the number of models increases; on the other hand numerous prior specifications can only exacerbate the well-known sensitivity to prior assignments, thus producing less dependable conclusions. Within the subjective framework, both difficulties can be counteracted by linking priors across models in order to achieve simplification and compatibility; we discuss links with related objective approaches. Given an encompassing, or full, model together with a prior on its parameter space, we review and summarize a few procedures for deriving priors under a submodel, namely marginalization, conditioning, and Kullback–Leibler projection. These techniques are illustrated and discussed with reference to variable selection in linear models adopting a conventional g-prior; comparisons with existing standard approaches are provided. Finally, the relative merits of each procedure are evaluated through simulated and real data sets.

Particle physics experiments such as those run in the Large Hadron Collider result in huge quantities of data, which are boiled down to a few numbers from which it is hoped that a signal will be detected. We discuss a simple probability model for this and derive frequentist and noninformative Bayesian procedures for inference about the signal. Both are highly accurate in realistic cases, with the frequentist procedure having the edge for interval estimation, and the Bayesian procedure yielding slightly better point estimates. We also argue that the significance, or p-value, function based on the modified likelihood root provides a comprehensive presentation of the information in the data and should be used for inference.

Many statistical problems involve mixture models and the need for computationally efficient methods to estimate the mixing distribution has increased dramatically in recent years. Newton [Sankhyā Ser. A 64 (2002) 306–322] proposed a fast recursive algorithm for estimating the mixing distribution, which we study as a special case of stochastic approximation (SA). We begin with a review of SA, some recent statistical applications, and the theory necessary for analysis of a SA algorithm, which includes Lyapunov functions and ODE stability theory. Then standard SA results are used to prove consistency of Newton’s estimate in the case of a finite mixture. We also propose a modification of Newton’s algorithm that allows for estimation of an additional unknown parameter in the model, and prove its consistency.

Spectral clustering is a broad class of clustering procedures in which an intractable combinatorial optimization formulation of clustering is “relaxed” into a tractable eigenvector problem, and in which the relaxed solution is subsequently “rounded” into an approximate discrete solution to the original problem. In this paper we present a novel margin-based perspective on multiway spectral clustering. We show that the margin-based perspective illuminates both the relaxation and rounding aspects of spectral clustering, providing a unified analysis of existing algorithms and guiding the design of new algorithms. We also present connections between spectral clustering and several other topics in statistics, specifically minimum-variance clustering, Procrustes analysis and Gaussian intrinsic autoregression.

There has been a split in the statistics community about the need for taking covariates into account in the design phase of a clinical trial. There are many advocates of using stratification and covariate-adaptive randomization to promote balance on certain known covariates. However, balance does not always promote efficiency or ensure more patients are assigned to the better treatment. We describe these procedures, including model-based procedures, for incorporating covariates into the design of clinical trials, and give examples where balance, efficiency and ethical considerations may be in conflict. We advocate a new class of procedures, covariate-adjusted response-adaptive (CARA) randomization procedures that attempt to optimize both efficiency and ethical considerations, while maintaining randomization. We review all these procedures, present a few new simulation studies, and conclude with our philosophy.

Myles Hollander was born in Brooklyn, New York, on March 21, 1941. He graduated from Carnegie Mellon University in 1961 with a B.S. in mathematics. In the fall of 1961, he entered the Department of Statistics, Stanford University, earning his M.S. in statistics in 1962 and his Ph.D. in statistics in 1965. He joined the Department of Statistics, Florida State University in 1965 and retired on May 31, 2007, after 42 years of service. He was department chair for nine years 1978–1981, 1999–2005. He was named Professor Emeritus at Florida State upon retirement in 2007.

Hollander served as Editor of the Journal of the American Statistical Association, Theory and Methods, 1994–1996, and was an Associate Editor for that journal from 1985 until he became Theory and Methods Editor-Elect in 1993. He also served on the editorial boards of the Journal of Nonparametric Statistics (1993–1997; 2003–2005) and Lifetime Data Analysis (1994–2007).

Hollander has published over 100 papers on nonparametric statistics, survival analysis, reliability theory, biostatistics, probability theory, decision theory, Bayesian statistics and multivariate analysis. He is grateful for the generous research support he has received throughout his career, most notably from the Office of Naval Research, the U.S. Air Force Office of Scientific Research, and the National Institutes of Health.

Myles Hollander has received numerous recognitions for his contributions to the profession. He was elected Fellow of the American Statistical Association (1972) and the Institute of Mathematical Statistics (1973), and became an elected member of the International Statistical Institute (1977). At Florida State University he was named Distinguished Researcher Professor (1996), he received the Professorial Excellence Award (1997), and in 1998 he was named the Robert O. Lawton Distinguished Professor, an award made to only one faculty member per year and the University’s highest faculty honor.

Myles Hollander was the Ralph A. Bradley Lecturer at the University of Georgia in 1999, and in 2003 he received the Gottfried E. Noether Senior Scholar Award in Nonparametric Statistics from the American Statistical Association. He was the Buckingham Scholar-in-Residence at Miami University, Oxford, Ohio in September, 1985, and had sabbatical visits at Stanford University (1972–1973; 1981–1982), the University of Washington (1989–1990) and the University of California at Davis (Spring, 2006). The following conversation took place in Myles Hollander’s office at the Department of Statistics, Florida State University, Tallahassee, on April 19, 2007.