Mathematical Statistics: Basic Ideas and Selected Topics PDF
Preview Mathematical Statistics: Basic Ideas and Selected Topics
Mathematical Statistics Basic Ideas and Selected Topics Volume II CHAPMAN & HALL/CRC Texts in Statistical Science Series Series Editors Francesca Dominici, Harvard School of Public Health, USA Julian J. Faraway, University of Bath, UK Martin Tanner, Northwestern University, USA Jim Zidek, University of British Columbia, Canada Statistical Theory: A Concise Introduction Statistics for Technology: A Course in Applied F. Abramovich and Y. Ritov Statistics, Third Edition C. Chatfield Practical Multivariate Analysis, Fifth Edition A. Afifi, S. May, and V.A. Clark Bayesian Ideas and Data Analysis: An Introduction for Scientists and Statisticians Practical Statistics for Medical Research D.G. Altman R. Christensen, W. Johnson, A. Branscum, and T.E. Hanson Interpreting Data: A First Course in Statistics Modelling Binary Data, Second Edition A.J.B. Anderson D. Collett Introduction to Probability with R Modelling Survival Data in Medical Research, K. Baclawski Third Edition D. Collett Linear Algebra and Matrix Analysis for Statistics Introduction to Statistical Methods for S. Banerjee and A. Roy Clinical Trials T.D. Cook and D.L. DeMets Mathematical Statistics: Basic Ideas and Selected Topics, Volume I, Second Edition Applied Statistics: Principles and Examples P. J. Bickel and K. A. Doksum D.R. Cox and E.J. Snell Mathematical Statistics: Basic Ideas and Multivariate Survival Analysis and Competing Selected Topics, Volume II Risks P. J. Bickel and K. A. Doksum M. Crowder Analysis of Categorical Data with R Statistical Analysis of Reliability Data C. R. Bilder and T. M. Loughin M.J. Crowder, A.C. Kimber, T.J. Sweeting, and R.L. Smith Statistical Methods for SPC and TQM D. Bissell An Introduction to Generalized Linear Models, Third Edition Introduction to Probability A.J. Dobson and A.G. Barnett J. K. Blitzstein and J. Hwang Nonlinear Time Series: Theory, Methods, and Bayesian Methods for Data Analysis, Applications with R Examples Third Edition R. Douc, E. Moulines, and D.S. Stoffer B.P. Carlin and T.A. Louis Introduction to Optimization Methods and Second Edition Their Applications in Statistics R. Caulcutt B.S. Everitt The Analysis of Time Series: An Introduction, Extending the Linear Model with R: Sixth Edition Generalized Linear, Mixed Effects and C. Chatfield Nonparametric Regression Models Introduction to Multivariate Analysis J.J. Faraway C. Chatfield and A.J. Collins Linear Models with R, Second Edition Problem Solving: A Statistician’s Guide, J.J. Faraway Second Edition A Course in Large Sample Theory C. Chatfield T.S. Ferguson Multivariate Statistics: A Practical Exercises and Solutions in Statistical Theory Approach L.L. Kupper, B.H. Neelon, and S.M. O’Brien B. Flury and H. Riedwyl Design and Analysis of Experiments with R Readings in Decision Analysis J. Lawson S. French Design and Analysis of Experiments with SAS Markov Chain Monte Carlo: J. Lawson Stochastic Simulation for Bayesian Inference, A Course in Categorical Data Analysis Second Edition T. Leonard D. Gamerman and H.F. Lopes Statistics for Accountants Bayesian Data Analysis, Third Edition S. Letchford A. Gelman, J.B. Carlin, H.S. Stern, D.B. Dunson, Introduction to the Theory of Statistical A. Vehtari, and D.B. Rubin Inference Multivariate Analysis of Variance and H. Liero and S. Zwanzig Repeated Measures: A Practical Approach for Statistical Theory, Fourth Edition Behavioural Scientists B.W. Lindgren D.J. Hand and C.C. Taylor Stationary Stochastic Processes: Theory and Practical Longitudinal Data Analysis Applications D.J. Hand and M. Crowder G. Lindgren Logistic Regression Models Statistics for Finance J.M. Hilbe E. Lindström, H. Madsen, and J. N. Nielsen Richly Parameterized Linear Models: The BUGS Book: A Practical Introduction to Additive, Time Series, and Spatial Models Bayesian Analysis Using Random Effects D. Lunn, C. Jackson, N. Best, A. Thomas, and J.S. Hodges D. Spiegelhalter Statistics for Epidemiology Introduction to General and Generalized N.P. Jewell Linear Models Stochastic Processes: An Introduction, H. Madsen and P. Thyregod Second Edition Time Series Analysis P.W. Jones and P. Smith H. Madsen The Theory of Linear Models Pólya Urn Models B. Jørgensen H. Mahmoud Principles of Uncertainty Randomization, Bootstrap and Monte Carlo J.B. Kadane Methods in Biology, Third Edition Graphics for Statistics and Data Analysis with R B.F.J. Manly K.J. Keen Introduction to Randomized Controlled Mathematical Statistics Clinical Trials, Second Edition K. Knight J.N.S. Matthews Introduction to Multivariate Analysis: Statistical Methods in Agriculture and Linear and Nonlinear Modeling Experimental Biology, Second Edition S. Konishi R. Mead, R.N. Curnow, and A.M. Hasted Nonparametric Methods in Statistics with SAS Statistics in Engineering: A Practical Approach Applications A.V. Metcalfe O. Korosteleva Statistical Inference: An Integrated Approach, Modeling and Analysis of Stochastic Systems, Second Edition Second Edition H. S. Migon, D. Gamerman, and V.G. Kulkarni F. Louzada Exercises and Solutions in Biostatistical Theory Beyond ANOVA: Basics of Applied Statistics L.L. Kupper, B.H. Neelon, and S.M. O’Brien R.G. Miller, Jr. A Primer on Linear Models Decision Analysis: A Bayesian Approach J.F. Monahan J.Q. Smith Applied Stochastic Modelling, Second Edition Analysis of Failure and Survival Data B.J.T. Morgan P. J. Smith Elements of Simulation Applied Statistics: Handbook of GENSTAT B.J.T. Morgan Analyses Probability: Methods and Measurement E.J. Snell and H. Simpson A. O’Hagan Applied Nonparametric Statistical Methods, Introduction to Statistical Limit Theory Fourth Edition A.M. Polansky P. Sprent and N.C. Smeeton Applied Bayesian Forecasting and Time Series Data Driven Statistical Methods Analysis P. Sprent A. Pole, M. West, and J. Harrison Generalized Linear Mixed Models: Statistics in Research and Development, Modern Concepts, Methods and Applications Time Series: Modeling, Computation, and W. W. Stroup Inference Survival Analysis Using S: Analysis of R. Prado and M. West Time-to-Event Data Introduction to Statistical Process Control M. Tableman and J.S. Kim P. Qiu Applied Categorical and Count Data Analysis Sampling Methodologies with Applications W. Tang, H. He, and X.M. Tu P.S.R.S. Rao Elementary Applications of Probability Theory, A First Course in Linear Model Theory Second Edition N. Ravishanker and D.K. Dey H.C. Tuckwell Essential Statistics, Fourth Edition Introduction to Statistical Inference and Its D.A.G. Rees Applications with R M.W. Trosset Stochastic Modeling and Mathematical Statistics: A Text for Statisticians and Understanding Advanced Statistical Methods Quantitative Scientists P.H. Westfall and K.S.S. Henning F.J. Samaniego Statistical Process Control: Theory and Statistical Methods for Spatial Data Analysis Practice, Third Edition O. Schabenberger and C.A. Gotway G.B. Wetherill and D.W. Brown Bayesian Networks: With Examples in R Generalized Additive Models: M. Scutari and J.-B. Denis An Introduction with R S. Wood Large Sample Methods in Statistics P.K. Sen and J. da Motta Singer Epidemiology: Study Design and Data Analysis, Third Edition Spatio-Temporal Methods in Environmental M. Woodward Epidemiology G. Shaddick and J.V. Zidek Practical Data Analysis for Designed Experiments B.S. Yandell Texts in Statistical Science Mathematical Statistics Basic Ideas and Selected Topics Volume II Peter J. Bickel University of California Berkley, California, USA Kjell A. Doksum University of Wisconsin Madison, Wisconsin, USA CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2016 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S. Government works Printed on acid-free paper Version Date: 20150909 International Standard Book Number-13: 978-1-4987-2268-1 (Pack - Book and Ebook) This book contains information obtained from authentic and highly regarded sources. Reasonable efforts have been made to publish reliable data and information, but the author and publisher cannot assume responsibility for the valid- ity of all materials or the consequences of their use. The authors and publishers have attempted to trace the copyright holders of all material reproduced in this publication and apologize to copyright holders if permission to publish in this form has not been obtained. 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Visit the Taylor & Francis Web site at http://www.taylorandfrancis.com and the CRC Press Web site at http://www.crcpress.com ToErichL.Lehmann CONTENTS PREFACETOTHE2016EDITION xv I INTRODUCTIONANDEXAMPLES 1 I.0 BasicIdeasandConventions 1 I.1 TestsofGoodnessofFitandtheBrownianBridge 5 I.2 TestingGoodnessofFittoParametricHypotheses 5 I.3 RegularParameters.MinimumDistanceEstimates 6 I.4 PermutationTests 8 I.5 EstimationofIrregularParameters 8 I.6 SteinandEmpiricalBayesEstimation 10 I.7 ModelSelection 11 I.8 ProblemsandComplements 15 I.9 Notes 20 7 TOOLSFORASYMPTOTICANALYSIS 21 7.1 WeakConvergenceinFunctionSpaces 21 7.1.1 StochasticProcessesandWeakConvergence 21 7.1.2 MaximalInequalities 28 7.1.3 EmpiricalProcessesonFunctionSpaces 31 7.2 TheDeltaMethodinInfiniteDimensionalSpace 38 7.2.1 InfluenceFunctions.TheGaˆteauxandFre´chetDerivatives 38 7.2.2 TheQuantileProcess 47 7.3 FurtherExpansions 51 7.3.1 ThevonMisesExpansion 51 7.3.2 TheHoeffdingandAnalysisofVarianceExpansions 54 7.4 ProblemsandComplements 62 7.5 Notes 72 ix
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