In many statistical applications, nonparametric modeling can provide insights into the features of a dataset that are not obtainable by other means. One successful approach involves the use of (univariate or multivariate) spline spaces. As a class, these methods have inherited much from classical tools for parametric modeling. For example, stepwise variable selection with spline basis terms is a simple scheme for locating knots (breakpoints) in regions where the data exhibit strong, local features. Similarly, candidate knot configurations (generated by this or some other search technique), are routinely evaluated with traditional selection criteria like AIC or BIC. In short, strategies typically applied in parametric model selection have proved useful in constructing flexible, low-dimensional models for nonparametric problems.

Until recently, greedy, stepwise procedures were most frequently suggested in the literature. Research into Bayesian variable selection, however, has given rise to a number of new spline-based methods that primarily rely on some form of Markov chain Monte Carlo to identify promising knot locations. In this paper, we consider various alternatives to greedy, deterministic schemes, and present a Bayesian framework for studying adaptation in the context of an extended linear model (ELM). Our major test cases are Logspline density estimation and (bivariate) Triogram regression models. We selected these because they illustrate a number of computational and methodological issues concerning model adaptation that arise in ELMs.

We review and compare block, sieve and local bootstraps for time series and thereby illuminate theoretical aspects of the procedures as well as their performance on finite-sample data. Our view is selective with the intention of providing a new and fair picture of some particular aspects of bootstrapping time series.

The generality of the block bootstrap is contrasted with sieve bootstraps. We discuss implementational advantages and disadvantages. We argue that two types of sieve often outperform the block method, each of them in its own important niche, namely linear and categorical processes. Local bootstraps, designed for nonparametric smoothing problems, are easy to use and implement but exhibit in some cases low performance.

Sample survey inference is historically concerned with finite-population parameters, that is, functions (like means and totals) of the observations for the individuals in the population. In scientific applications, however, interest usually focuses on the “superpopulation” parameters associated with a stochastic mechanismhypothesized to generate the observations in the population rather than the finite-population parameters. Two relevant findings discussed in this paper are that (1) with stratified sampling, it is not sufficient to drop finite-population correction factors from standard design-based variance formulas to obtain appropriate variance formulas for superpopulation inference, and (2) with cluster sampling, standard design-based variance formulas can dramatically underestimate superpopulation variability, even with a small sampling fraction of the final units. A literature review of inference for superpopulation parameters is given, with emphasis on why these findings have not been previously appreciated. Examples are provided for estimating superpopulation means, linear regression coefficients and logistic regression coefficients using U.S. data from the 1987 National Health Interview Survey, the third National Health and Nutrition Examination Survey and the 1986 National Hospital Discharge Survey.

The eponym “Walker Circulation” refers to a concept used by atmospheric scientists and oceanographers in providing a physical explanation for the El Niño–Southern Oscillation phenomenon, whereas the eponym “Yule–Walker equations” refers to properties satisfied by the autocorrelations of an autoregressive process. But how many statisticians (or, for that matter, atmospheric scientists) are aware that the “Walker” in both terms refers to the same individual, Sir Gilbert Thomas Walker, and that these two appellations arose in conjunction with the same research on the statistical prediction of climate? Like George Udny Yule (the “Yule” in Yule– Walker), Walker’s motivation was to devise a statistical model that exhibited quasiperiodic behavior. The original assessments of Walker’s work, both in the meteorology and in statistics, were somewhat negative. With hindsight, it is argued that his research should be viewed as quite successful.

Kantilal Vardichand Mardia was born on April 3, 1935, in Sirohi, Rajasthan, India. He earned his B.Sc. degree in mathematics from Ismail Yusuf College–University of Bombay, in 1955, M.Sc. degrees in statistics and in pure mathematics from University of Bombay in 1957 and University of Poona in 1961, respectively, and Ph.D. degrees in statistics from the University of Rajasthan and the University of Newcastle, respectively, in 1965 and 1967. For significant contributions in statistics, he was awarded a D.Sc. degree from the University of Newcastle in 1973. He started his career as an Assistant Lecturer in the Institute of Science, Bombay and went to Newcastle as a Commonwealth Scholar. After receiving the Ph.D. degree from Newcastle, he joined the University of Hull as a lecturer in statistics in 1967, later becoming a reader in statistics in 1971. He was appointed a Chair Professor in Applied Statistics at the University of Leeds in 1973 and was the Head of the Department of Statistics during 1976–1993, and again from 1997 to the present. Professor Mardia has made pioneering contributions in many areas of statistics including multivariate analysis, directional data analysis, shape analysis, and spatial statistics. He has been credited for path-breaking contributions in geostatistics, imaging, machine vision, tracking, and spatio-temporal modeling, to name a few. He was instrumental in the founding of the Center of Medical Imaging Research in Leeds and he holds the position of a joint director of this internationally eminent center. He has pushed hard in creating exchange programs between Leeds and other scholarly centers such as the University of Granada, Spain, and the Indian Statistical Institute, Calcutta. He has written several scholarly books and edited conference proceedings and other special volumes. But perhaps he is best known for his books: Multivariate Analysis (coauthored with John Kent and John Bibby, 1979, Academic Press), Statistics of Directional Data (second edition with Peter Jupp, 1999, Wiley) and Statistical Shape Analysis (coauthored with Ian Dryden, 1998, Wiley). The conferences and workshops he has been organizing in Leeds for a number of years have had significant impacts on statistics and its interface with IT (information technology). He is dynamic and his sense of humor is unmistakable. He is a world traveler. Among other places, he has visited Princeton University, the University of Michigan, Harvard University, the University of Granada, Penn State and the University of Connecticut. He has given keynote addresses and invited lectures in international conferences on numerous occasions. He has been on the editorial board of statistical, as well as image related, journals including the IEEE Transactions on Pattern Analysis and Machine Intelligence, Journal of Environmental and Ecological Statistics, Journal of Statistical Planning and Inference and Journal of Applied Statistics. He has been elected a Fellow of the American Statistical Association, a Fellow of the Institute of Mathematical Statistics, and a Fellow of the American Dermatoglyphic Association. He is also an elected member of the International Statistical Institute and a Senior Member of IEEE. Professor Mardia retired on September 30, 2000 to take a full-time post as Senior Research Professor at Leeds—a new position especially created for him.