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Modern survival analysis and more general event history analysis may be effectively handled in the mathematical framework of counting processes, stochastic integration, martingale central limit theory and product integration. This book presents this theory, which has been the subject of an intense research activity during the past one-and-a- half decades. The exposition of the theory is integrated with careful presentation of many practical examples, almost exclusively from the authors' own experience, with detailed numerical and graphical illustrations. Statistical Models Based on Counting Processes may be viewed as a research monograph for mathematical statisticians and biostatisticians, although almost all methods are given in concrete detail to be used in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuarial mathematicians, reliabilty engineers and biologists). Much of the material has so far only been available in the journal literature (if at all), and so a wide variety of researchers will find this an invaluable survey of the subject."This book is a masterful account of the counting process approach...is certain to be the standard reference for the area, and should be on the bookshelf of anyone interested in event-history analysis." International Statistical Institute Short Book Reviews "...this impressive reference, which contains a a wealth of powerful mathematics, practical examples, and analytic insights, as well as a complete integration of historical developments and recent advances in event history analysis." Journal of the American Statistical Association
Del 1581 - Lecture Notes in Mathematics
Lectures on Probability Theory
Ecole d'Ete de Probabilites de Saint-Flour XXII - 1992
Häftad, Engelska, 1994
535 kr
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This book contains work-outs of the notes of three 15-hour courses of lectures which constitute surveys on the concerned topics given at the St. Flour Probability Summer School in July 1992. The first course, by D. Bakry, is concerned with hypercontractivity properties and their use in semi-group theory, namely Sobolev and Log Sobolev inequalities, with estimations on the density of the semi-groups. The second one, by R.D. Gill, is about statistics on survival analysis; it includes product-integral theory, Kaplan-Meier estimators, and a look at cryptography and generation of randomness. The third one, by S.A. Molchanov, covers three aspects of random media: homogenization theory, localization properties and intermittency. Each of these chapters provides an introduction to and survey of its subject.