Statistical estimation for truncated exponential families / Masafumi Akahira.
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 trunc...
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Full Text (via Springer) |
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| Format: | eBook |
| Language: | English |
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Singapore :
Springer,
2017.
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| Series: | SpringerBriefs in statistics. JSS research series in statistics.
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| 100 | 1 | |a Akahira, Masafumi, |d 1945- |e author. |0 http://id.loc.gov/authorities/names/n80141196 |1 http://isni.org/isni/0000000108958860. | |
| 245 | 1 | 0 | |a Statistical estimation for truncated exponential families / |c Masafumi Akahira. |
| 264 | 1 | |a Singapore : |b Springer, |c 2017. | |
| 300 | |a 1 online resource (xi, 122 pages) : |b illustrations. | ||
| 336 | |a text |b txt |2 rdacontent. | ||
| 337 | |a computer |b c |2 rdamedia. | ||
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| 347 | |a text file |b PDF |2 rda. | ||
| 490 | 1 | |a SpringerBriefs in statistics, JSS research series in statistics, |x 2191-544X. | |
| 504 | |a Includes bibliographical references and index. | ||
| 505 | 0 | |a Preface; Acknowledgements; Contents; 1 Asymptotic Estimation for Truncated Exponential Families; 1.1 Models with Nuisance Parameters and Their Differences; 1.2 One-Sided Truncated Exponential Family; 1.3 Two-Sided Truncated Exponential Family; References; 2 Maximum Likelihood Estimation of a Natural Parameter for a One-Sided TEF; 2.1 Introduction; 2.2 Preliminaries; 2.3 MLE ML (Sd (Bof a Natural Parameter (Sk (BWhen a Truncation Parameter (Sd (Bis Known; 2.4 Bias-Adjusted MLE ML* of (Sk (BWhen (Sd (Bis Unknown; 2.5 MCLE MCL of (Sk (BWhen (Sd (Bis Unknown; 2.6 Second-Order Asymptotic Comparison Among ML (Sd (B, ML*, and MCL. | |
| 505 | 8 | |a 2.7 Examples2.8 Concluding Remarks; 2.9 Appendix A1; 2.10 Appendix A2; References; 3 Maximum Likelihood Estimation of a Natural Parameter for a Two-Sided TEF; 3.1 Introduction; 3.2 Preliminaries; 3.3 MLE ML (Sd (B, (Sp (Bof (Sk (BWhen Truncation Parameters (Sd (Band (Sp (Bare Known; 3.4 Bias-Adjusted MLE ML* of (Sk (BWhen (Sd (Band (Sp (Bare Unknown; 3.5 MCLE MCL of (Sk (BWhen (Sd (Band (Sp (Bare Unknown; 3.6 Second-Order Asymptotic Comparison Among ML (Sd (B, (Sp (B, ML*, and MCL; 3.7 Examples; 3.8 Concluding Remarks; 3.9 Appendix B1; 3.10 Appendix B2; References; 4 Estimation of a Truncation Parameter for a One-Sided TEF; 4.1 Introduction. | |
| 505 | 8 | |a 4.2 Preliminaries4.3 Bias-Adjusted MLE ML* (Sk (Bof (Sd (BWhen (Sk (Bis Known; 4.4 Bias-Adjusted MLE ML* of (Sd (BWhen (Sk (Bis Unknown; 4.5 Second-Order Asymptotic Loss of ML* Relative to ML* (Sk (B; 4.6 Examples; 4.7 Concluding Remarks; 4.8 Appendix C; References; 5 Estimation of a Truncation Parameter for a Two-Sided TEF; 5.1 Introduction; 5.2 Preliminaries; 5.3 Bias-Adjusted MLE ML* (Sk (B, (Sd (Bof (Sp (BWhen (Sk (Band (Sd (Bare Known; 5.4 Bias-Adjusted MLE ML* (Sd (Bof (Sp (BWhen (Sk (Bis Unknown and (Sd (Bis Known; 5.5 Bias-Adjusted MLE ML* of (Sp (BWhen (Sk (Band (Sd (Bare Unknown ; 5.6 Second-Order Asymptotic Losses of ML* and ML* (Sd (BRelative to ML* (Sk (B, (Sd (B. | |
| 505 | 8 | |a 5.7 Examples5.8 Concluding Remarks; 5.9 Appendix D; References; 6 Bayesian Estimation of a Truncation Parameter for a One-Sided TEF; 6.1 Introduction; 6.2 Formulation and Assumptions; 6.3 Bayes Estimator B, (Sk (Bof (Sd (BWhen (Sk (Bis Known; 6.4 Bayes Estimator B, ML of (Sd (BWhen (Sk (Bis Unknown; 6.5 Examples; 6.6 Concluding Remarks; 6.7 Appendix E; Reference; Index. | |
| 520 | |a 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.-- |c Provided by publisher. | ||
| 588 | 0 | |a Online resource; title from PDF title page (SpringerLink, viewed August 3, 2017) | |
| 650 | 0 | |a Estimation theory. |0 http://id.loc.gov/authorities/subjects/sh85044957. | |
| 650 | 7 | |a Estimation theory. |2 fast |0 (OCoLC)fst00915531. | |
| 773 | 0 | |t Springer eBooks. | |
| 776 | 0 | 8 | |i Print version: |a Akahira, Masafumi. |t Statistical estimation for truncated exponential families. |d Singapore : Springer, 2017 |z 9811052956 |z 9789811052958 |w (OCoLC)988279002. |
| 830 | 0 | |a SpringerBriefs in statistics. |p JSS research series in statistics. |0 http://id.loc.gov/authorities/names/no2016036062. | |
| 856 | 4 | 0 | |u https://colorado.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-981-10-5296-5 |z Full Text (via Springer) |
| 880 | 8 | |6 505-00/(S |a 2.7 Examples2.8 Concluding Remarks; 2.9 Appendix A1; 2.10 Appendix A2; References; 3 Maximum Likelihood Estimation of a Natural Parameter for a Two-Sided TEF; 3.1 Introduction; 3.2 Preliminaries; 3.3 MLE MLγ, ν of θ When Truncation Parameters γ and ν are Known; 3.4 Bias-Adjusted MLE ML* of θ When γ and ν are Unknown; 3.5 MCLE MCL of θ When γ and ν are Unknown; 3.6 Second-Order Asymptotic Comparison Among MLγ, ν, ML*, and MCL; 3.7 Examples; 3.8 Concluding Remarks; 3.9 Appendix B1; 3.10 Appendix B2; References; 4 Estimation of a Truncation Parameter for a One-Sided TEF; 4.1 Introduction. | |
| 880 | 8 | |6 505-00/(S |a 4.2 Preliminaries4.3 Bias-Adjusted MLE ML*θ of γ When θ is Known; 4.4 Bias-Adjusted MLE ML* of γ When θ is Unknown; 4.5 Second-Order Asymptotic Loss of ML* Relative to ML*θ; 4.6 Examples; 4.7 Concluding Remarks; 4.8 Appendix C; References; 5 Estimation of a Truncation Parameter for a Two-Sided TEF; 5.1 Introduction; 5.2 Preliminaries; 5.3 Bias-Adjusted MLE ML*θ, γ of ν When θ and γ are Known; 5.4 Bias-Adjusted MLE ML*γ of ν When θ is Unknown and γ is Known; 5.5 Bias-Adjusted MLE ML* of ν When θ and γ are Unknown ; 5.6 Second-Order Asymptotic Losses of ML* and ML*γ Relative to ML*θ, γ | |
| 880 | 8 | |6 505-00/(S |a 5.7 Examples5.8 Concluding Remarks; 5.9 Appendix D; References; 6 Bayesian Estimation of a Truncation Parameter for a One-Sided TEF; 6.1 Introduction; 6.2 Formulation and Assumptions; 6.3 Bayes Estimator B, θ of γ When θ is Known; 6.4 Bayes Estimator B, ML of γ When θ is Unknown; 6.5 Examples; 6.6 Concluding Remarks; 6.7 Appendix E; Reference; Index. | |
| 880 | 0 | |6 505-00/(S |a Preface; Acknowledgements; Contents; 1 Asymptotic Estimation for Truncated Exponential Families; 1.1 Models with Nuisance Parameters and Their Differences; 1.2 One-Sided Truncated Exponential Family; 1.3 Two-Sided Truncated Exponential Family; References; 2 Maximum Likelihood Estimation of a Natural Parameter for a One-Sided TEF; 2.1 Introduction; 2.2 Preliminaries; 2.3 MLE MLγ of a Natural Parameter θ When a Truncation Parameter γ is Known; 2.4 Bias-Adjusted MLE ML* of θ When γ is Unknown; 2.5 MCLE MCL of θ When γ is Unknown; 2.6 Second-Order Asymptotic Comparison Among MLγ, ML*, and MCL. | |
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