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E-grāmata: Statistical Estimation for Truncated Exponential Families

  • Formāts: EPUB+DRM
  • Sērija : SpringerBriefs in Statistics
  • Izdošanas datums: 26-Jul-2017
  • Izdevniecība: Springer Verlag, Singapore
  • Valoda: eng
  • ISBN-13: 9789811052965
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Statistical Estimation for Truncated Exponential FamiliesPalielināt
  • Formāts: EPUB+DRM
  • Sērija : SpringerBriefs in Statistics
  • Izdošanas datums: 26-Jul-2017
  • Izdevniecība: Springer Verlag, Singapore
  • Valoda: eng
  • ISBN-13: 9789811052965
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This book presents new findings on nonregular statistical estimation. Unlike other books on this topic, its major emphasis is on helping readers understand the meaning and implications of both regularity and irregularity through a certain family of distributions. In particular, it focuses on a truncated exponential family of distributions with a natural parameter and truncation parameter as a typical nonregular family. This focus includes the (truncated) Pareto distribution, which is widely used in various fields such as finance, physics, hydrology, geology, astronomy, and other disciplines. The family is essential in that it links both regular and nonregular distributions, as it becomes a regular exponential family if the truncation parameter is known. The emphasis is on presenting new results on the maximum likelihood estimation of a natural parameter or truncation parameter if one of them is a nuisance parameter. In order to obtain more information on the truncation, the Bayesian approach is also considered. Further, the application to some useful truncated distributions is discussed. The illustrated clarification of the nonregular structure provides researchers and practitioners with a solid basis for further research and applications.

1 Asymptotic Estimation for Truncated Exponential Families
1(6)
1.1 Models with Nuisance Parameters and Their Differences
1(3)
1.2 One-Sided Truncated Exponential Family
4(1)
1.3 Two-Sided Truncated Exponential Family
5(2)
References
6(1)
2 Maximum Likelihood Estimation of a Natural Parameter for a One-Sided TEF
7(28)
2.1 Introduction
7(1)
2.2 Preliminaries
8(1)
2.3 MLE θγML of a Natural Parameter θ When a Truncation Parameter γ is Known
9(1)
2.4 Bias-Adjusted MLE θML* of θ When γ is Unknown
10(1)
2.5 MCLE θMCL of θ When γ is Unknown
11(2)
2.6 Second-Order Asymptotic Comparison Among θγML, θML*, and θMCL
13(1)
2.7 Examples
14(9)
2.8 Concluding Remarks
23(1)
2.9 Appendix Al
24(7)
2.10 Appendix A2
31(4)
References
34(1)
3 Maximum Likelihood Estimation of a Natural Parameter for a Two-Sided TEF
35(30)
3.1 Introduction
35(1)
3.2 Preliminaries
36(1)
3.3 MLE θγ,νML of θ When γ and ν are Unknown
36(1)
3.4 Bias-Adjusted MLE θMC* of θ When γ and ν are Unknown
37(2)
3.5 MCLE θMCL of θ When γ and ν are Unknown
39(1)
3.6 Second-Order Asymptotic Comparison Among θγνML, θML*, and θMCL
40(1)
3.7 Examples
41(11)
3.8 Concluding Remarks
52(1)
3.9 Appendix B1
53(8)
3.10 Appendix B2
61(4)
References
64(1)
4 Estimation of a Truncation Parameter for a One-Sided TEF
65(14)
4.1 Introduction
65(1)
4.2 Preliminaries
65(1)
4.3 Bias-Adjusted MLE γθML* of γ When θ is Known
66(1)
4.4 Bias-Adjusted MLE γML* of γ When θ is Unknown
67(1)
4.5 Second-Order Asymptotic Loss of γML*, Relative to γθML*
68(1)
4.6 Examples
69(5)
4.7 Concluding Remarks
74(1)
4.8 Appendix C
75(4)
References
78(1)
5 Estimation of a Truncation Parameter for a Two-Sided TEF
79(24)
5.1 Introduction
79(1)
5.2 Preliminaries
80(1)
5.3 Bias-Adjusted MLE νθ,γML* of ν When θ are Known
80(1)
5.4 Bias-Adjusted MLE νγML* of ν When θ is Unknown and γ is Known
81(3)
5.5 Bias-Adjusted MLE νML* of ν When θ and γ are Unknown
84(2)
5.6 Second-Order Asymptotic Losses of νML* and νγML* Relative to νθ,γML*
86(1)
5.7 Examples
87(10)
5.8 Concluding Remarks
97(1)
5.9 Appendix D
98(5)
References
102(1)
6 Bayesian Estimation of a Truncation Parameter for a One-Sided TEF
103(18)
6.1 Introduction
103(1)
6.2 Formulation and Assumptions
103(1)
6.3 Bayes Estimator γB,θ of γ When θ is Known
104(1)
6.4 Bayes Estimator γB, θML of γ When θ is Unknown
105(2)
6.5 Examples
107(6)
6.6 Concluding Remarks
113(1)
6.7 Appendix E
114(7)
Reference
120(1)
Index 121
Masafumi Akahira, Professor Emeritus, Institute of Mathematics, University of Tsukuba 
Biežāk uzdotie jautājumi par e-grāmatām Biežāk uzdotie jautājumi par e-grāmatām
Permanent link: https://www.kriso.lv/db/97898110529656e.html
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