Elements of Large-Sample TheoryElements of Large Sample Theory provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology written at an elementary level. The book is suitable for students at the Master's level in statistics and in aplied fields who have a background of two years of calculus. E.L. Lehmann is Professor of Statistics Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands, and the University of Chicago. Also available: E.L. Lehmann and George Casella, Theory at Point Estimation, Second Edition. Springer-Verlag New York, Inc., 1998, 640 pp., Cloth, ISBN 0-387-98502-6. E.L. Lehmann, Testing Statistical Hypotheses, Second Edition. Springer-Verlag New York, Inc., 1997, 624 pp., Cloth, ISBN 0-387-94919-4. |
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ˆFn ˆfn(y alternative analogous approximation assumptions of Theorem asymptotic distribution asymptotic level asymptotic normality asymptotic variance asymptotically equivalent Bayes estimator bias binomial bivariate normal bootstrap central limit theorem coefficient confidence intervals consider consistent estimator continuous convergence in probability corresponding covariance matrix defined denote derivative determine distribution F efficient estimator Example expected squared error finite follows given hence Hint holds hypothesis i.i.d. according independent Jeffreys prior joint distribution Lemma Let X1 likelihood equation likelihood ratio linear multinomial multivariate non-singular normal distribution obtained one-sample parameters Poisson Poisson distribution population proof Prove random variables rejection region replaced respectively result sample satisfies Section sequence situation statistics Suppose symmetric t-test Table tends in law two-sample U-statistic vector Wald test Wilcoxon Xn be i.i.d.