Mathematical Theory of Statistics
eBook - PDF

Mathematical Theory of Statistics

Statistical Experiments and Asymptotic Decision Theory

  1. 504 pages
  2. English
  3. PDF
  4. Available on iOS & Android
eBook - PDF

Mathematical Theory of Statistics

Statistical Experiments and Asymptotic Decision Theory

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Yes, you can access Mathematical Theory of Statistics by Helmut Strasser in PDF and/or ePUB format, as well as other popular books in Mathematics & Mathematics General. We have over one million books available in our catalogue for you to explore.

Information

Publisher
De Gruyter
Year
2011
Print ISBN
9783110102581
eBook ISBN
9783110850826
Edition
1
Topic
Mathematics
Subtopic
Mathematics General
Index
Mathematics

Table of contents

  1. Chapter 1: Basic Notions on Probability Measures
  2. 1. Decomposition of probability measures
  3. 2. Distances between probability measures
  4. 3. Topologies and σ-fields on sets of probability measures
  5. 4. Separable sets of probability measures
  6. 5. Transforms of bounded Borel measures
  7. 6. Miscellaneous results
  8. Chapter 2: Elementary Theory of Testing Hypotheses
  9. 7. Basic definitions
  10. 8. Neyman-Pearson theory for binary experiments
  11. 9. Experiments with monotone likelihood ratios
  12. 10. The generalized lemma of Neyman-Pearson
  13. 11. Exponential experiments of rank 1
  14. 12. Two-sided testing for exponential experiments: Part 1
  15. 13. Two-sided testing for exponential experiments: Part 2
  16. Chapter 3: Binary Experiments
  17. 14. The error function
  18. 15. Comparison of binary experiments
  19. 16. Representation of experiment types
  20. 17. Concave functions and Mellin transforms
  21. 18. Contiguity of probability measures
  22. Chapter 4: Sufficiency, Exhaustivity, and Randomizations
  23. 19. The idea of sufficiency
  24. 20. Pairwise sufficiency and the factorization theorem
  25. 21. Sufficiency and topology
  26. 22. Comparison of dominated experiments by testing problems
  27. 23. Exhaustivity
  28. 24. Randomization of experiments
  29. 25. Statistical isomorphism
  30. Chapter 5: Exponential Experiments
  31. 26. Basic facts
  32. 27. Conditional tests
  33. 28. Gaussian shifts with nuisance parameters
  34. Chapter 6: More Theory of Testing
  35. 29. Complete classes of tests
  36. 30. Testing for Gaussian shifts
  37. 31. Reduction of testing problems by invariance
  38. 32. The theorem of Hunt and Stein
  39. Chapter 7: Theory of estimation
  40. 33. Basic notions of estimation
  41. 34. Median unbiased estimation for Gaussian shifts
  42. 35. Mean unbiased estimation
  43. 36. Estimation by desintegration
  44. 37. Generalized Bayes estimates
  45. 38. Full shift experiments and the convolution theorem
  46. 39. The structure model
  47. 40. Admissibility of estimators
  48. Chapter 8: General decision theory
  49. 41. Experiments and their L-spaces
  50. 42. Decision functions
  51. 43. Lower semicontinuity
  52. 44. Risk functions
  53. 45. A general minimax theorem
  54. 46. The minimax theorem of decision theory
  55. 47. Bayes solutions and the complete class theorem
  56. 48. The generalized theorem of Hunt and Stein
  57. Chapter 9: Comparison of experiments
  58. 49. Basic concepts
  59. 50. Standard decision problems
  60. 51. Comparison of experiments by standard decision problems
  61. 52. Concave function criteria
  62. 53. Hellinger transforms and standard measures
  63. 54. Comparison of experiments by testing problems
  64. 55. The randomization criterion
  65. 56. Conical measures
  66. 57. Representation of experiments
  67. 58. Transformation groups and invariance
  68. 59. Topological spaces of experiments
  69. Chapter 10: Asymptotic decision theory
  70. 60. Weakly convergent sequences of experiments
  71. 61. Contiguous sequences of experiments
  72. 62. Convergence in distribution of decision functions
  73. 63. Stochastic convergence of decision functions
  74. 64. Convergence of minimum estimates
  75. 65. Uniformly integrable experiments
  76. 66. Uniform tightness of generalized Bayes estimates
  77. 67. Convergence of generalized Bayes estimates
  78. Chapter 11: Gaussian shifts on Hilbert spaces
  79. 68. Linear stochastic processes and cylinder set measures
  80. 69. Gaussian shift experiments
  81. 70. Banach sample spaces
  82. 71. Testing for Gaussian shifts
  83. 72. Estimation for Gaussian shifts
  84. 73. Testing and estimation for Banach sample spaces
  85. Chapter 12: Differentiability and asymptotic expansions
  86. 74. Stochastic expansion of likelihood ratios
  87. 75. Differentiable curves
  88. 76. Differentiable experiments
  89. 77. Conditions for differentiability
  90. 78. Examples of differentiable experiments
  91. 79. The stochastic expansion of a differentiable experiment
  92. Chapter 13: Asymptotic normality
  93. 80. Asymptotic normality
  94. 81. Exponential approximation and asymptotic sufficiency
  95. 82. Application to testing hypotheses
  96. 83. Application to estimation
  97. 84. Characterization of central sequences
  98. Appendix: Notation and terminology
  99. References
  100. List of symbols
  101. Author index
  102. Subject index