| Description |
1 online resource (321 p.) |
| Series |
Chapman and Hall/CRC Texts in Statistical Science Series |
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Chapman and Hall/CRC Texts in Statistical Science Series
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| Contents |
Cover -- Half Title -- Series Page -- Title Page -- Copyright Page -- Table of Contents -- Preface -- 1 Random Variables and Vectors -- 1.1 Random Variables, Their Distributions and Their Attributes -- 1.2 The Quantile Function -- 1.3 Random Vectors, Their Distributions and Properties -- 1.4 Transformations -- Functions of Random Variables -- 1.5 Some Common Univariate Distributions -- 1.6 The Multinormal Distribution -- 1.7 Stochastic Ordering -- 1.8 The Change-of-Measure Identity -- 1.9 Computing with R, Simulation Studies -- Appendix: Some Special Functions |
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A.1 The Gamma and Beta Functions -- A.2 The Digamma Function and Euler's Constant -- A.3 The Trigamma Function -- Exercises -- 2 Weak Convergence -- 2.1 Sequences of Random Variables -- Weak Convergence -- 2.2 The O[sub(p)]/o[sub(p)] Notation -- 2.3 Other Criteria for Weak Convergence -- 2.4 The Continuous Mapping Theorem -- 2.5 Convergence of Expectations -- 2.6 The "Delta Method" -- 2.7 Variance-Stabilizing Transformations -- 2.8 Weak Convergence of Sequences of Random Vectors -- 2.9 Example: Estimation for the Lognormal Distribution |
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2.10 Example: Estimation of Effect Size for Power Calculations -- 2.11 Example: Combining Estimators, Weighted Means -- 2.12 Further Theorems on Weak Convergence -- 2.13 Variables That Are Independent but Not Identically Distributed -- 2.14 The Weak Law of Large Numbers -- Proof by Truncation -- Appendix I: Taylor Series Expansions -- Appendix II: The Order (O/o) Notation in Analysis -- Appendix III: Weak Convergence of Sample Quantile Functions -- Exercises -- 3 Asymptotic Linearity of Statistics -- 3.1 Asymptotic Linearity -- 3.2 Deriving Asymptotically Linear Expansions |
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3.3 The Bahadur Representation of a Sample Quantile -- 3.4 U-statistics:- Central Limit Theorem and Asymptotic Linearity -- 3.5 Gâteaux Differentiation -- 3.6 Some Further Examples -- 3.7 Final Comments -- Exercises -- 4 Local Analysis -- 4.1 Motivation -- 4.2 Local Asymptotic Normality-Random Sampling Case -- 4.3 Local Asymptotic Normality-General Case -- 4.4 LeCam's Third Lemma -- Exercises -- 5 Large Sample Estimation -- 5.1 Moment and Quantile Estimation -- 5.2 Exact Unbiased Estimation from Finite Samples, the Cramér-Rao Bound -- 5.3 Consistency, Root-n Consistency and Asymptotic Normality |
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5.4 Joint Asymptotic Normality, Regular Estimators and Efficiency -- 5.5 Constructing Efficient Estimates -- 5.6 M-estimation -- 5.7 Bibliographic Notes -- Appendix: A Counterexample to the Efficiency of Maximum Likelihood -- A.1 Estimating the Proportion Red When Sampling Colored Balls from an Urn -- A.2 A Regular Estimation Problem with an Inconsistent Maximum Likelihood Estimator -- Exercises -- 6 Estimating Parameters of Interest -- 6.1 Effective Scores -- 6.2 Estimating a Parametric Function -- 6.3 Estimation Under Constraints on the Parameter -- 6.4 Relative Efficiency |
| Summary |
This book provides an accessible but rigorous introduction to asymptotic theory in parametric statistical models. The book is based on lecture notes prepared by the first author, subsequently edited, expanded and updated by the second author. Includes a large number of exercises |
| Notes |
Description based upon print version of record |
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6.5 Brief Bibliographic Notes |
| Form |
Electronic book
|
| Author |
Oakes, David
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| ISBN |
9781498726115 |
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1498726119 |
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