Asymptotics in Statistics
Autor Lucien Le Cam, Grace Lo Yangen Limba Engleză Paperback – 17 oct 2012
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Specificații
ISBN-13: 9781461270300
ISBN-10: 1461270308
Pagini: 304
Ilustrații: XIII, 287 p.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.46 kg
Ediția:Second Edition 2000
Editura: Springer
Locul publicării:New York, NY, United States
ISBN-10: 1461270308
Pagini: 304
Ilustrații: XIII, 287 p.
Dimensiuni: 155 x 235 x 17 mm
Greutate: 0.46 kg
Ediția:Second Edition 2000
Editura: Springer
Locul publicării:New York, NY, United States
Public țintă
ResearchCuprins
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.
Recenzii
From the reviews:
SHORT BOOK REVIEWS
"It is a very valuable book giving a coherent view of the basic concept and tools of the asymptotic theory in statistical inference."
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
"…short and mathematically very sophisticated. Its approach is modern and undoubtedly profound."
SHORT BOOK REVIEWS
"It is a very valuable book giving a coherent view of the basic concept and tools of the asymptotic theory in statistical inference."
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
"…short and mathematically very sophisticated. Its approach is modern and undoubtedly profound."