Erik Torgersen - Böcker

This is author-approved bcc: The papers in this volume were contributed in honor of Lucien Le Cam on the occasion of his 70th birthday. They reflect the immense influence that his work has had on modern statistics. The papers include discussions of Le Cam's seminal ideas, historical perspectives, and contributions to current research. They reach back two centuries, with a new translation of a paper of Daniel Bernoulli, and they reach forward to new ideas about semiparametric theory and wavelets. The volume begins with the paper of Aalen, which describes Le Cam's role in the founding of the martingale analysis of point processes, and ends with the paper of Yu, which explores the position of just one of Le Cam's ideas in modern semiparametric theory. The other 27 papers touch on other areas-such as local asymptotic normality, contiguity, efficiency, admissibility, minimaxity, empirical process theory, and biological medical, and meterological applications - where Le Cam's insights have been the foundations on which a theory has been built.

There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians.

There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians.