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The preface outlines coverage of minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, bias and mean square error, UMVUEs, and the Fréchet-Cramér–Rao lower bound, along with large-sample theory, likelihood ratio tests, UMP tests, and the Neyman–Pearson lemma. 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Olive  \nStatistical Theory and Inference  \nStatistical Theory and Inference  \nDavid J. Olive  \nStatistical Theory and Inference  \n1 3  \nDavid J. Olive Department of Mathematics Southern Illinois University Carbondale, IL, USA  \nISBN 978-3-319-04971-7 ISBN 978-3-319-04972-4 (eBook)  \nDOI 10.1007/978-3-319-04972-4  \nSpringer Cham Heidelberg New York Dordrecht London Library of Congress Control Number: 2014934894  \nMathematics Subject Classification (2010): 62 01, 62B05, 62F03, 62F10, 62F12  \n© Springer International Publishing Switzerland 2014  \nThis work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law.  \nThe use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use.  \nWhile the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein.  \nPrinted on acid-free paper  \nSpringer is part of Springer Science+Business Media ([www.springer.com](www.springer.com))  \nPreface  \nMany math and some statistics departments offer a one-semester graduate course in statistical theory using texts such as Casella and Berger (2002), Bickel and Doksum (2007) or Mukhopadhyay (2000, 2006) . The course typically covers minimal and complete sufficient statistics, maximum likelihood estimators (MLEs), method of moments, bias and mean square error, uniform minimum variance unbiased estimators (UMVUEs) and the Frchet–Cramr–Rao lower bound (FCRLB), an introduction to large sample theory, likelihood ratio tests, and uniformly most powerful (UMP) tests and the Neyman–Pearson Lemma. A major goal of this text is to make these topics much more accessible to students by using the theory of exponential families.  \nOne of the most important uses of exponential families is that the theory often provides two methods for doing inference. For example, minimal sufficient statistics can be found with either the Lehmann Scheff theorem or by finding T from the exponential family parameterization. Similarly, if Y1 ,..., Yn are iid from a oneparameter regular exponential family with complete sufficient statistic T (Y), then one-sidedUMP tests can be found by using the Neyman–Pearson lemma or by using exponential family theory.  \nThe prerequisite for this text is a calculus-based course in statistics at the level of Hogg and Tanis (2005), Larsen and Marx (2011), Wackerly et al. (2008), or Walpole et al. (2006) . Also see Arnold (1990), Gathwaite et al. (2002), Spanos (1999), Wasserman (2004), and Welsh (1996) .  \nThe following intermediate texts are especially re","cbCaitievnW4wYoP","https://ap.wps.com/l/cbCaitievnW4wYoP","pdf",4213868,438,"English","# Preface\n## Course overview and goals\n## Exponential-family based inference\n## Prerequisites and recommended texts","[{\"question\":\"What main goal does the book aim to achieve for students?\",\"answer\":\"The text aims to make key statistical theory and inference topics much more accessible by using exponential family theory.\"},{\"question\":\"Which core topics in statistical theory are highlighted in the preface?\",\"answer\":\"It highlights minimal and complete sufficient statistics, maximum likelihood estimators, method of moments, UMVUEs, bias and mean square error, the Fréchet-Cramér–Rao lower bound, and large-sample theory.\"},{\"question\":\"What prerequisite background does the book require?\",\"answer\":\"The prerequisite is a calculus-based course in statistics at the level of common graduate statistics texts, with additional guidance on probability and real analysis for specific chapters.\"}]","Statistical Theory and Inference | PDF",1104]