دانلود کتاب Mathematical Theory of Statistics: Statistical Experiments and Asymptotic Decision Theory

فهرست مطالب :

Chapter 1: Basic Notions on Probability Measures\n1. Decomposition of probability measures\n2. Distances between probability measures\n3. Topologies and σ-fields on sets of probability measures\n4. Separable sets of probability measures\n5. Transforms of bounded Borel measures\n6. Miscellaneous results\nChapter 2: Elementary Theory of Testing Hypotheses\n7. Basic definitions\n8. Neyman-Pearson theory for binary experiments\n9. Experiments with monotone likelihood ratios\n10. The generalized lemma of Neyman-Pearson\n11. Exponential experiments of rank 1\n12. Two-sided testing for exponential experiments: Part 1\n13. Two-sided testing for exponential experiments: Part 2\nChapter 3: Binary Experiments\n14. The error function\n15. Comparison of binary experiments\n16. Representation of experiment types\n17. Concave functions and Mellin transforms\n18. Contiguity of probability measures\nChapter 4: Sufficiency, Exhaustivity, and Randomizations\n19. The idea of sufficiency\n20. Pairwise sufficiency and the factorization theorem\n21. Sufficiency and topology\n22. Comparison of dominated experiments by testing problems\n23. Exhaustivity\n24. Randomization of experiments\n25. Statistical isomorphism\nChapter 5: Exponential Experiments\n26. Basic facts\n27. Conditional tests\n28. Gaussian shifts with nuisance parameters\nChapter 6: More Theory of Testing\n29. Complete classes of tests\n30. Testing for Gaussian shifts\n31. Reduction of testing problems by invariance\n32. The theorem of Hunt and Stein\nChapter 7: Theory of estimation\n33. Basic notions of estimation\n34. Median unbiased estimation for Gaussian shifts\n35. Mean unbiased estimation\n36. Estimation by desintegration\n37. Generalized Bayes estimates\n38. Full shift experiments and the convolution theorem\n39. The structure model\n40. Admissibility of estimators\nChapter 8: General decision theory\n41. Experiments and their L-spaces\n42. Decision functions\n43. Lower semicontinuity\n44. Risk functions\n45. A general minimax theorem\n46. The minimax theorem of decision theory\n47. Bayes solutions and the complete class theorem\n48. The generalized theorem of Hunt and Stein\nChapter 9: Comparison of experiments\n49. Basic concepts\n50. Standard decision problems\n51. Comparison of experiments by standard decision problems\n52. Concave function criteria\n53. Hellinger transforms and standard measures\n54. Comparison of experiments by testing problems\n55. The randomization criterion\n56. Conical measures\n57. Representation of experiments\n58. Transformation groups and invariance\n59. Topological spaces of experiments\nChapter 10: Asymptotic decision theory\n60. Weakly convergent sequences of experiments\n61. Contiguous sequences of experiments\n62. Convergence in distribution of decision functions\n63. Stochastic convergence of decision functions\n64. Convergence of minimum estimates\n65. Uniformly integrable experiments\n66. Uniform tightness of generalized Bayes estimates\n67. Convergence of generalized Bayes estimates\nChapter 11: Gaussian shifts on Hilbert spaces\n68. Linear stochastic processes and cylinder set measures\n69. Gaussian shift experiments\n70. Banach sample spaces\n71. Testing for Gaussian shifts\n72. Estimation for Gaussian shifts\n73. Testing and estimation for Banach sample spaces\nChapter 12: Differentiability and asymptotic expansions\n74. Stochastic expansion of likelihood ratios\n75. Differentiable curves\n76. Differentiable experiments\n77. Conditions for differentiability\n78. Examples of differentiable experiments\n79. The stochastic expansion of a differentiable experiment\nChapter 13: Asymptotic normality\n80. Asymptotic normality\n81. Exponential approximation and asymptotic sufficiency\n82. Application to testing hypotheses\n83. Application to estimation\n84. Characterization of central sequences\nAppendix: Notation and terminology\nReferences\nList of symbols\nAuthor index\nSubject index