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Asymptotics in Statistics Some Basic Concepts

by Sara van de Geer. Also, we did not include material due to David Donoho, lain Johnstone, and their school. We found our­ selves unprepared to write a distillate of the material. We did touch briefly on "nonparametrics," but not on "semiparamet­ rics." This is because we feel t...

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Bibliographic Details
Main Authors: Le Cam, Lucien, Lo Yang, Grace (Author)
Format: eBook
Language:English
Published: New York, NY Springer New York 2000, 2000
Edition:2nd ed. 2000
Series:Springer Series in Statistics
Subjects:
Statistical Theory And Methods
Statistics 
Applications Of Mathematics
Mathematics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • 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 Bernstein—von Mises Phenomenon
  • 8.4 A Bernstein—von Mises Result for the i.i.d. Case
  • 8.5 Bayes Procedures Behave Miserably
  • 8.6 Historical Remarks
  • Author Index

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