Elements of LargeSample TheoryElements of Large Sample Theory provides a unified treatment of firstorder largesample 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. SpringerVerlag New York, Inc., 1998, 640 pp., Cloth, ISBN 0387985026. E.L. Lehmann, Testing Statistical Hypotheses, Second Edition. SpringerVerlag New York, Inc., 1997, 624 pp., Cloth, ISBN 0387949194. 
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Contents
Mathematical Background  1 
Convergence in Probability and in Law  47 
Performance of Statistical Tests  133 
Estimation  219 
Multivariate Extensions  277 
Nonparametric Estimation  363 
Efficient Estimators and Tests  451 
Appendix  571 
591  
Author Index  609 
615  
Common terms and phrases
alternatives An(F analogous apply approximation assumptions of Theorem asymptotic distribution asymptotic level asymptotic normality asymptotic variance asymptotically equivalent Bayes estimator bias bootstrap central limit theorem coefficient confidence intervals consider consistent estimator continuous convergence in probability corresponding covariance matrix defined delta method denote depends derivative determine distribution F efficiency Example exists finite fixed fn(y function given hence Hint holds hypothesis i.i.d. according independent Jeffreys prior joint distribution largesample Lemma Let Xi likelihood equation limit distribution linear median multinomial multivariate normal distribution obtained onesample parameters Poisson Poisson distribution population preceding problem proof Prove random variables rejection region replaced respectively result right side satisfies Section sequence situation Suppose symmetric ttest Table tend to infinity tends in law test of H tion twosample vectors Wilcoxon test Xn be i.i.d.
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Page 596  On the Probable Errors of Frequency Constants," Journal of the Royal Statistical Society, vol. 71, June 1908, p. 389. The article quoted is one of a series on the subject published in vol. 71 of the Journal, pp. 381, 499 and 651, and vol. 72, p. 81.
Page 597  RA Fisher. Theory of statistical estimation. Proceedings of the Cambridge Philosophical Society, 22:700725, 1925.