David Victor Hinkley, 1944–2019

David Hinkley, who died peacefully at his home in California on January 11th, 2019, made important and broad ranging contributions to statistical theory and methods.

He was born on September 10th, 1944, in Kent, the youngest of three children of Eric and Edna Hinkley; Eric served in the Royal Air Force during the Second World War. After leaving Beckenham and Penge Grammar School for Boys, David studied mathematics and statistics at the University of Birmingham, where he was taught by John Nelder, David Wishart and Henry Daniels, who suggested that he undertake a doctorate at Imperial College, London, under the supervision of David Cox. Imperial College was then a rapidly expanding hub for statistical activity, and by the time David had published his first paper, on the efficiency of least squares estimators, he had been appointed to a junior lecturership. He received his doctorate in 1969 for a thesis on change points in sequences of random variables and in regression, papers on which followed in rapid succession during a period at Stanford University from 1969 to 1971. He married Betty Blake in 1970, and their daughter Sara was born in 1971, just before they returned to London. There, amid many other projects, David worked with David Cox on Theoretical Statistics, published in 1974.

This book was arguably the first modern treatment of the foundations and theory of statistics and remains a landmark for the study of what was then called mathematical statistics. Its scope, its illustration of statistical principles through a series of compelling examples highlighting the strengths and weaknesses of different approaches to inference, its emphasis on likelihood and its even-handed treatment of conditional, frequentist and Bayesian approaches have given it lasting influence on subsequent generations of students and scholars. Although its eschewal of mathematical technicalities and dogma infuriated some reviewers, it was immediately recognized as a major contribution. The difficulty and substance of its problems, many taken from research papers, led to the publication in 1978 of a book of solutions that remains worth studying in its own right. Russian editions of both books later appeared.

David was now established as an outstandingly broad, able and productive scholar, and in 1973, shortly after the birth of their son Steve, the family moved to the University of Minnesota. During this period David became interested in the jackknife, a harbinger of his later work on resampling methods. Fisher's work was a strong influence and the organization of a reading group led to the appearance in 1980 of R. A. Fisher: an Appreciation, edited jointly with Stephen Fienberg. David contributed two articles to this collection of essays, on Fisher's monumental 1925 paper on estimation and on his development of conditional inference. These topics were closely related to David's research, which had led in 1978 to the publication in Biometrika of a paper joint with Bradley Efron that introduced what is now called the Efron–Hinkley ancillary. Much previous work on asymptotic inference, and much textbook discussion even now, treats the observed information and its expectation as interchangeable, but Fisher had realized that the former could play the role of an approximate ancillary statistic, so inferences that condition on its value are more relevant to the particular data set under study. Efron and Hinkley provided convincing empirical evidence for this in one-parameter models and discussed the role of the ratio of the observed and expected information quantities. This paper, and David's 1980 advocacy of conditioning in his review of likelihood inference in the Canadian Journal of Statistics, played an important role in stimulating the blossoming, in the 1980s, of so-called small sample asymptotics, which can provide highly accurate parametric inferences from tiny data sets. His 1979 Annals of Statistics paper likewise galvanized research on predictive likelihood, with the goal of providing an appropriate frequentist counterpart to the posterior predictive density that is used in Bayesian inference.

In 1983 David became the Jane and Roland Blumberg Centennial Professor of Mathematics at the University of Texas at Austin, where his presence attracted active young researchers. There his interests in resampling expanded to the bootstrap, resulting in the introduction of efficient bootstrap methods including the use of saddlepoint approximation to avoid simulation entirely, the advocacy of conditioning in resampling and a paper read to the Royal Statistical Society in 1988. An outgrowth of this activity was the 1997 publication, joint with Anthony Davison, of Bootstrap Methods and Their Application. This book, which was originally stimulated by the widespread interest in a short course that had been given at a conference in Neuchâtel in 1992, gave a broad perspective on when and how bootstrap methods might be safely applied, and included discussions of many topics that had not previously been addressed in the bootstrap literature. It was at once recognized as an important text and remains a standard reference.

In 1989 he moved from Austin to the new Department of Statistics at the University of Oxford as its inaugural Professor of Statistical Science. Although Oxford had housed luminaries such as Peter Armitage, Norman Bailey, Maurice Bartlett, David Finney, David Kendall, John Kingman and Richard Peto, and despite the presence of statistical scientists in fields such as economics, epidemiology and the social sciences, statistics there was fragmented and disorganized. Under David's leadership and that of Brian Ripley and John Gittins, the new department grew rapidly in size and as a focus for statistical activity. David found the broader Oxford environment difficult, however, and in 1995 moved to the University of California, Santa Barbara, from where he retired in 2014.

A distinctive, upright figure and brilliant lecturer, David illuminated any topic to which he turned. His bracing analyses are exemplified by his writing on the Box–Cox transform: around 1980 a paper in the Journal of the American Statistical Association argued that the effect of selecting the transformation parameter by using the data should be taken into account in measuring the uncertainty of regression effects, but, in discussion related to current investigation of inference after model selection, David and others argued strongly that this is scientifically nonsensical.

His broad vision, lucidity, excellent judgement and the esteem in which he was held made him a natural candidate for committees and editorial work. He had university leadership roles from early in his career and served on national committees in the USA and UK. His professional service included chairing the Research Section Committee of the Royal Statistical Society from 1989 to 1991, editorships of the Annals of Statistics and of Biometrika, and associate editorships of several major journals. In addition to his major publications, he edited several books that remain worthwhile reading.

His honours included the prestigious Committee of Presidents of Statistical Societies award in 1984—the statistical equivalent of a Fields Medal—and Fellowships of the American Statistical Association, the American Association for the Advancement of Science and the Institute of Mathematical Statistics, for which he gave two Medallion Lectures.

David and Betty divorced in 1991; she died in 2015. He is survived by Sara and Steve, his four grandchildren, who delighted him and with whom he spent happy times watching soccer matches and visiting the US national parks and California coast, an elder sister and other family in the UK. His brother died in 2011.

David listened to BBC radio each evening and was anguished by recent political events. He was a generous, stimulating and enduringly supportive mentor for younger colleagues, and they and his students, friends and family will miss his penetrating clarity, his lively and wide-ranging intellect, his wry humour and his passions for soccer, nature and classical music.

I thank Sara Hinkley and Allan Stewart-Oaten for their help in preparing this obituary.

A. C. Davison