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 US, 1990 |
Connect to | http://dx.doi.org/10.1007/978-1-4684-0377-0 |
Descript | VIII, 180 p. online resource |
1 Introduction -- 2 Experiments, Deficiencies, Distances -- 2.1 Comparing risk functions -- 2.2 Likelihood ratios. Blackwellโs representation -- 2.3 Historical Remarks -- 3 Contiguity โ 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 Waldโs 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