04893nam 2200709 450 991081132960332120200520144314.01-118-85728-31-118-85737-2(CKB)2550000001298090(EBL)1687768(SSID)ssj0001253374(PQKBManifestationID)11709936(PQKBTitleCode)TC0001253374(PQKBWorkID)11293376(PQKB)10863007(MiAaPQ)EBC1687768(Au-PeEL)EBL1687768(CaPaEBR)ebr10870261(CaONFJC)MIL608508(OCoLC)879947306(PPN)191455342(EXLCZ)99255000000129809020140927h20142014 uy 0engur|n|---|||||txtccrInformation and exponential families in statistical theory /O. Barndorff-Nielsen2nd ed.Chichester, England :John Wiley & Sons,2014.©20141 online resource (250 p.)Wiley Series in Probability and StatisticsDescription based upon print version of record.1-118-85750-X 1-306-77257-5 Includes bibliographical references and indexes.Cover; Title Page; Copyright Page; Contents; CHAPTER 1 INTRODUCTION; 1.1 Introductory remarks and outline; 1.2 Some mathematical prerequisites; 1.3 Parametric models; Part I Lods functions and inferential separation; CHAPTER 2 LIKELIHOOD AND PLAUSIBILITY; 2.1 Universality; 2.2 Likelihood functions and plausibility functions; 2.3 Complements; 2.4 Notes; CHAPTER 3 SAMPLE-HYPOTHESIS DUALITY AND LODS FUNCTIONS; 3.1 Lods functions; 3.2 Prediction functions; 3.3 Independence; 3.4 Complements; 3.5 Notes; CHAPTER 4 LOGIC OF INFERENTIAL SEPARATION. ANCILLARITY AND SUFFICIENCY4.1 On inferential separation. Ancillarity and sufficiency4.2 B-sufficiency and B-ancillarity; 4.3 Nonformation; 4.4 S-, G-, and M-ancillarity and -sufficiency; 4.5 Quasi-ancillarity and Quasi-sufficiency; 4.6 Conditional and unconditional plausibility functions; 4.7 Complements; 4.8 Notes; Part II Convex analysis, unimodality, and Laplace transforms; CHAPTER 5 CONVEX ANALYSIS; 5.1 Convex sets; 5.2 Convex functions; 5.3 Conjugate convex functions; 5.4 Differential theory; 5.5 Complements; CHAPTER 6 LOG-CONCAVITY AND UNIMODALITY; 6.1 Log-concavity6.2 Unimodality of continuous-type distributions6.3 Unimodality of discrete-type distributions; 6.4 Complements; CHAPTER 7 LAPLACE TRANSFORMS; 7.1 The Laplace transform; 7.2 Complements; Part III Exponential families; CHAPTER 8 INTRODUCTORY THEORY OF EXPONENTIAL FAMILIES; 8.1 First properties; 8.2 Derived families; 8.3 Complements; 8.4 Notes; CHAPTER 9 DUALITY AND EXPONENTIAL FAMILIES; 9.1 Convex duality and exponential families; 9.2 Independence and exponential families; 9.3 Likelihood functions for full exponential families; 9.4 Likelihood functions for convex exponential families9.5 Probability functions for exponential families9.6 Plausibility functions for full exponential families; 9.7 Prediction functions for full exponential families; 9.8 Complements; 9.9 Notes; CHAPTER 10 INFERENTIAL SEPARATION AND EXPONENTIAL FAMILIES; 10.1 Quasi-ancillarity and exponential families; 10.2 Cuts in general exponential families; 10.3 Cuts in discrete-type exponential families; 10.4 S-ancillarity and exponential families; 10.5 M-ancillarity and exponential families; 10.6 Complement; 10.7 Notes; References; Author index; Subject indexFirst published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions. Wiley series in probability and statistics.Exponential families (Statistics)Sufficient statisticsDistribution (Probability theory)Exponential functionsExponential families (Statistics)Sufficient statistics.Distribution (Probability theory)Exponential functions.519.5Barndorff-Nielsen O.1724975MiAaPQMiAaPQMiAaPQBOOK9910811329603321Information and exponential families4127493UNINA