Asymptotics in Statistics

This book presents a coherent introduction to the subject of asymptotic statistics as it has developed in the past 50 years. Professor Le Cam is one of the major researchers in this area and this book will make his results accessible to graduate students and researchers in statistics.

Autorentext
Lucien Le Cam is Professor of Statistics and Mathematics (Emeritus) at the University of California, Berkeley. He is the author of numerous papers on "Asymptotics and Asymptotic Methods in Statistical Decision Theory". He was co-editor, with J. Neyman and E. Scott of the Berkeley Symposia on Mathematical Statistics and Probability. Grace Lo Yang is Professor, Department of Mathe

Zusammenfassung
This is the second edition of a coherent introduction to the subject of asymptotic statistics as it has developed over the past 50 years. Much of the material has been taught in a second year graduate course at Berkeley for 30 years.

Inhalt
1 Introduction.- 2 Experiments, Deficiencies, Distances v.- 2.1 Comparing Risk Functions.- 2.2 Deficiency and Distance between Experiments.- 2.3 Likelihood Ratios and Blackwell's Representation.- 2.4 Further Remarks on the Convergence of Distri butions of Likelihood Ratios.- 2.5 Historical Remarks.- 3 Contiguity Hellinger Transforms.- 3.1 Contiguity.- 3.2 Hellinger Distances, Hellinger Transforms.- 3.3 Historical Remarks.- 4 Gaussian Shift and Poisson Experiments.- 4.1 Introduction.- 4.2 Gaussian Experiments.- 4.3 Poisson Experiments.- 4.4 Historical Remarks.- 5 Limit Laws for Likelihood Ratios.- 5.1 Introduction.- 5.2 Auxiliary Results.- 5.3 Limits for Binary Experiments.- 5.4 Gaussian Limits.- 5.5 Historical Remarks.- 6 Local Asymptotic Normality.- 6.1 Introduction.- 6.2 Locally Asymptotically Quadratic Families.- 6.3 A Method of Construction of Estimates.- 6.4 Some Local Bayes Properties.- 6.5 Invariance and Regularity.- 6.6 The LAMN and LAN Conditions.- 6.7 Additional Remarks on the LAN Conditions.- 6.8 Wald's Tests and Confidence Ellipsoids.- 6.9 Possible Extensions.- 6.10 Historical Remarks.- 7 Independent, Identically Distributed Observations.- 7.1 Introduction.- 7.2 The Standard i.i.d. Case: Differentiability in Quadratic Mean.- 7.3 Some Examples.- 7.4 Some Nonparametric Considerations.- 7.5 Bounds on the Risk of Estimates.- 7.6 Some Cases Where the Number of Observations Is Random.- 7.7 Historical Remarks.- 8 On Bayes Procedures.- 8.1 Introduction.- 8.2 Bayes Procedures Behave Nicely.- 8.3 The Bernsteinvon Mises Phenomenon.- 8.4 A Bernsteinvon Mises Result for the i.i.d. Case.- 8.5 Bayes Procedures Behave Miserably.- 8.6 Historical Remarks.- Author Index.