## 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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### 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 large-sample Lemma Let Xi likelihood equation limit distribution linear median multinomial multivariate normal distribution obtained one-sample parameters Poisson Poisson distribution population preceding problem proof Prove random variables rejection region replaced respectively result right side satisfies Section sequence situation Suppose symmetric t-test Table tend to infinity tends in law test of H tion two-sample vectors Wilcoxon test Xn be i.i.d.

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Page 597 - Limiting distributions in simple random sampling from a finite population', Pub. Math. Inst., Hungarian Acad.

Page 594 - Cohen, Statistical Power Analysis for the Behavioral Sciences, Academic Press, New York, 1969.

Page 591 - The Theory of Linear Models and Multivariate Analysis . John Wiley & Sons, New York.

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, 22:700-725, 1925.