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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| 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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Table of Contents:
- 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.
- 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.
- 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.
- 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.
- 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.
- 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
- 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.
- 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.