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Field name	Details
Dewey Class	519
Title	Asymptotics in Statistics ([EBook] :) : Some Basic Concepts / / by Lucien Le Cam, Grace Lo Yang.
Author	Cam, Lucien Le
Added Personal Name	Yang, Grace Lo author.
Other name(s)	SpringerLink (Online service)
Publication	New York, NY : : Springer US, , 1990.
Physical Details	VIII, 180 p. : online resource.
Series	Springer Series in Statistics 0172-7397
ISBN	9781468403770
Summary Note	In the summer of 1968 one of the present authors (LLC) had the pleasure of giving a sequence of lectures at the University of Mon treal. Lecture notes were collected and written out by Drs. Catherine Doleans, Jean Haezendonck and Roch Roy. They were published in French by the Presses of the University of Montreal as part of their series of Seminaires de Mathematiques Superieures. Twenty years later it was decided that a Chinese translation could be useful, but upon prodding by Professor Shanti Gupta at Purdue we concluded that the notes should be updated and rewritten in English and in Chinese. The present volume is the result of that effort. We have preserved the general outline of the lecture notes, but we have deleted obsolete material and sketched some of the results acquired during the past twenty years. This means that while the original notes concentrated on the LAN situation we have included here some results of Jeganathan and others on the LAMN case. Also included are versions of the Hajek-Le Cam asymptotic minimax and convolution theorems with some of their implications. We have not attempted to give complete coverage of the subject and have often stated theorems without indicating their proofs.:
Contents note	1 Introduction -- 2 Experiments, Deficiencies, Distances -- 2.1 Comparing risk functions -- 2.2 Likelihood ratios. Blackwell’s representation -- 2.3 Historical Remarks -- 3 Contiguity — Hellinger Transforms -- 3.1 Contiguity -- 3.2 Hellinger distances, Hellinger transforms -- 3.3 Historical Remarks -- 4 Limit Laws for Likelihood Ratios Obtained from Independent Observations -- 4.1 Introduction -- 4.2 Limit laws in the binary case -- 4.3 Historical Remarks -- 5 Locally Asymptotically Normal Families -- 5.1 1 Introduction -- 5.2 Locally asymptotically quadratic families -- 5.3 A method of construction of estimates -- 5.4 Some local Bayes properties -- 5.5 Invariance and regularity -- 5.6 The LAMN and LAN conditions -- 5.7 Additional remarks on the LAN conditions -- 5.8 Wald’s tests and confidence ellipsoids -- 5.9 Possible extensions -- 5.10 Historical Remarks -- 6 Independent, Identically Distributed Observations -- 6.1 Introduction -- 6.2 The standard i.i.d. case. Differentiability in quadratic mean -- 6.3 Some examples -- 6.4 Some nonparametric considerations -- 6.5 Bounds on the risk of estimates -- 6.6 Some cases where the number of observations is random -- 6.7 Historical Remarks -- 7 On Bayes Procedures -- 7.1 Introduction -- 7.2 Bayes procedures behave nicely -- 7.3 The Bernstein-von Mises Phenomenon -- 7.4 A Bernstein-von Mises result for the i.i.d. case -- 7.5 Bayes procedures behave miserably -- 7.6 Historical Remarks -- 8 Bibliography -- Author Index.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-1-4684-0377-0
Links to Related Works	Subject References: Applications of Mathematics . Applied mathematics . Engineering mathematics . Mathematics . Statistical Theory and Methods . Statistics . Authors: Cam, Lucien Le . Yang, Grace Lo . Corporate Authors: SpringerLink (Online service) . Series: Springer Series in Statistics . Classification: 519 .

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Asymptotics in Statistics: Some Basic Concepts /

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