UID:
almahu_9947360002802882
Format:
Online-Ressource (xii, 492 p)
Edition:
Online-Ausg. Palo Alto, Calif ebrary 2011 Electronic reproduction; Available via World Wide Web
ISBN:
0899250289 (U.S.)
,
9783110102581
,
9783110850826
Series Statement:
De Gruyter studies in mathematics 7
Content:
Mathematical Theory of Statistics
Note:
Includes bibliographical references (p. [478]-482) and indexes
,
12. Two-sided testing for exponential experiments: Part 113. Two-sided testing for exponential experiments: Part 2; Chapter 3: Binary Experiments; 14. The error function; 15. Comparison of binary experiments; 16. Representation of experiment types; 17. Concave functions and Mellin transforms; 18. Contiguity of probability measures; Chapter 4: Sufficiency, Exhaustivity, and Randomizations; 19. The idea of sufficiency; 20. Pairwise sufficiency and the factorization theorem; 21. Sufficiency and topology; 22. Comparison of dominated experiments by testing problems; 23. Exhaustivity.
,
24. Randomization of experiments25. Statistical isomorphism; Chapter 5: Exponential Experiments; 26. Basic facts; 27. Conditional tests; 28. Gaussian shifts with nuisance parameters; Chapter 6: More Theory of Testing; 29. Complete classes of tests; 30. Testing for Gaussian shifts; 31. Reduction of testing problems by invariance; 32. The theorem of Hunt and Stein; Chapter 7: Theory of estimation; 33. Basic notions of estimation; 34. Median unbiased estimation for Gaussian shifts; 35. Mean unbiased estimation; 36. Estimation by desintegration; 37. Generalized Bayes estimates.
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38. Full shift experiments and the convolution theorem39. The structure model; 40. Admissibility of estimators; Chapter 8: General decision theory; 41. Experiments and their L-spaces; 42. Decision functions; 43. Lower semicontinuity; 44. Risk functions; 45. A general minimax theorem; 46. The minimax theorem of decision theory; 47. Bayes solutions and the complete class theorem; 48. The generalized theorem of Hunt and Stein; Chapter 9: Comparison of experiments; 49. Basic concepts; 50. Standard decision problems; 51. Comparison of experiments by standard decision problems.
,
52. Concave function criteria53. Hellinger transforms and standard measures; 54. Comparison of experiments by testing problems; 55. The randomization criterion; 56. Conical measures; 57. Representation of experiments; 58. Transformation groups and invariance; 59. Topological spaces of experiments; Chapter 10: Asymptotic decision theory; 60. Weakly convergent sequences of experiments; 61. Contiguous sequences of experiments; 62. Convergence in distribution of decision functions; 63. Stochastic convergence of decision functions; 64. Convergence of minimum estimates.
,
65. Uniformly integrable experiments.
,
Chapter 1: Basic Notions on Probability Measures; 1. Decomposition of probability measures; 2. Distances between probability measures; 3. Topologies and σ-fields on sets of probability measures; 4. Separable sets of probability measures; 5. Transforms of bounded Borel measures; 6. Miscellaneous results; Chapter 2: Elementary Theory of Testing Hypotheses; 7. Basic definitions; 8. Neyman-Pearson theory for binary experiments; 9. Experiments with monotone likelihood ratios; 10. The generalized lemma of Neyman-Pearson; 11. Exponential experiments of rank 1.
Language:
English
DOI:
10.1515/9783110850826
URL:
http://dx.doi.org/10.1515/9783110850826
URL:
http://www.degruyter.com/doi/book/10.1515/9783110850826
URL:
http://www.degruyter.com/search?f_0=isbnissn&q_0=9783110850826&searchTitles=true
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