Author | Cam, Lucien Le. author |
---|---|
Title | Asymptotics in Statistics [electronic resource] : Some Basic Concepts / by Lucien Le Cam, Grace Lo Yang |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2000 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-1-4612-1166-2 |
Descript | XIII, 287 p. online resource |
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 โ 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 Bernsteinโvon Mises Phenomenon -- 8.4 A Bernsteinโvon Mises Result for the i.i.d. Case -- 8.5 Bayes Procedures Behave Miserably -- 8.6 Historical Remarks -- Author Index