Author: Andreas N. Philippou
Publisher:
ISBN:
Category :
Languages : en
Pages : 350

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Book Description

Author: Andreas N. Philippou
Publisher:
ISBN:
Category : Asymptotic distribution (Probability theory)
Languages : en
Pages : 19

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Book Description

Author: LIH-WEN HUANG
Publisher:
ISBN:
Category :
Languages : en
Pages : 59

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Book Description

Author: Byeong U. Park
Publisher:
ISBN:
Category : Estimation theory
Languages : en
Pages : 12

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Book Description

Author: Robert Bartoszynski
Publisher: John Wiley & Sons
ISBN: 1119243815
Category : Mathematics
Languages : en
Pages : 592

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Book Description
Updated classic statistics text, with new problems and examples Probability and Statistical Inference, Third Edition helps students grasp essential concepts of statistics and its probabilistic foundations. This book focuses on the development of intuition and understanding in the subject through a wealth of examples illustrating concepts, theorems, and methods. The reader will recognize and fully understand the why and not just the how behind the introduced material. In this Third Edition, the reader will find a new chapter on Bayesian statistics, 70 new problems and an appendix with the supporting R code. This book is suitable for upper-level undergraduates or first-year graduate students studying statistics or related disciplines, such as mathematics or engineering. This Third Edition: Introduces an all-new chapter on Bayesian statistics and offers thorough explanations of advanced statistics and probability topics Includes 650 problems and over 400 examples - an excellent resource for the mathematical statistics class sequence in the increasingly popular "flipped classroom" format Offers students in statistics, mathematics, engineering and related fields a user-friendly resource Provides practicing professionals valuable insight into statistical tools Probability and Statistical Inference offers a unique approach to problems that allows the reader to fully integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic.

Author: I. V. Basawa
Publisher: Springer Science & Business Media
ISBN: 1461255058
Category : Mathematics
Languages : en
Pages : 183

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Book Description
This monograph contains a comprehensive account of the recent work of the authors and other workers on large sample optimal inference for non-ergodic models. The non-ergodic family of models can be viewed as an extension of the usual Fisher-Rao model for asymptotics, referred to here as an ergodic family. The main feature of a non-ergodic model is that the sample Fisher information, appropriately normed, converges to a non-degenerate random variable rather than to a constant. Mixture experiments, growth models such as birth processes, branching processes, etc. , and non-stationary diffusion processes are typical examples of non-ergodic models for which the usual asymptotics and the efficiency criteria of the Fisher-Rao-Wald type are not directly applicable. The new model necessitates a thorough review of both technical and qualitative aspects of the asymptotic theory. The general model studied includes both ergodic and non-ergodic families even though we emphasise applications of the latter type. The plan to write the monograph originally evolved through a series of lectures given by the first author in a graduate seminar course at Cornell University during the fall of 1978, and by the second author at the University of Munich during the fall of 1979. Further work during 1979-1981 on the topic has resolved many of the outstanding conceptual and technical difficulties encountered previously. While there are still some gaps remaining, it appears that the mainstream development in the area has now taken a more definite shape.

Author: A. W. van der Vaart
Publisher: Cambridge University Press
ISBN: 9780521784504
Category : Mathematics
Languages : en
Pages : 470

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Book Description
This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics.

Author: Sonja Greven
Publisher: Cuvillier Verlag
ISBN: 3867274916
Category : Inference
Languages : en
Pages : 153

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Book Description

Author: Halbert White
Publisher: Cambridge University Press
ISBN: 9780521574464
Category : Business & Economics
Languages : en
Pages : 396

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Book Description
This book examines the consequences of misspecifications for the interpretation of likelihood-based methods of statistical estimation and interference. The analysis concludes with an examination of methods by which the possibility of misspecification can be empirically investigated.

Author: W. Jackson Hall
Publisher: CRC Press
ISBN: 1498726119
Category : Mathematics
Languages : en
Pages : 330

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Book Description
This book provides an accessible but rigorous introduction to asymptotic theory in parametric statistical models. Asymptotic results for estimation and testing are derived using the “moving alternative” formulation due to R. A. Fisher and L. Le Cam. Later chapters include discussions of linear rank statistics and of chi-squared tests for contingency table analysis, including situations where parameters are estimated from the complete ungrouped data. This book is based on lecture notes prepared by the first author, subsequently edited, expanded and updated by the second author. Key features: • Succinct account of the concept of “asymptotic linearity” and its uses • Simplified derivations of the major results, under an assumption of joint asymptotic normality • Inclusion of numerical illustrations, practical examples and advice • Highlighting some unexpected consequences of the theory • Large number of exercises, many with hints to solutions Some facility with linear algebra and with real analysis including ‘epsilon-delta’ arguments is required. Concepts and results from measure theory are explained when used. Familiarity with undergraduate probability and statistics including basic concepts of estimation and hypothesis testing is necessary, and experience with applying these concepts to data analysis would be very helpful.