Essentials of statistical inference:
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Cambridge [u.a.]
Cambridge Univ. Press
2010
|
| Edition: | 1. paperback ed. |
| Series: | Cambridge series in statistical and probabilistic mathematics
[16] |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 225 S. graph. Darst. |
| ISBN: | 9780521548663 0521839718 9780521839716 |
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Record in the Search Index
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| adam_text | Contents Preface page ix 1 Introduction 1 2 Decision theory 2.1 Formulation 2.2 The risk fonction 2.3 Criteria for a good decision rule 2.4 Randomised decision rules 2.5 Finite decision problems 2.6 Finding minimax rules in general 2.7 Admissibility of Bayes rules 4 2.8 3 Bayesian methods 3.1 Fundamental elements 3.2 The general form of Bayes rules 3.3 Back to minimax... 3.4 Shrinkage and the James-Stein estimator 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 4 Problems Empirical Bayes Choice of prior distributions Computational techniques Hierarchical modelling Predictive distributions Data example: Coal-mining disasters Data example: Gene expression data Problems Hypothesis testing 4.1 Formulation of the hypothesis testing problem 4.2 The Neyman-Pearson Theorem 4.3 Uniformly most powerful tests 4.4 Bayes factors 4.5 Problems 4 5 7 11 11 18 19 19 22 22 28 32 33 38 39 42 48 52 55 57 60 65 65 68 69 73 78
vi Contents 5 Special models 5.1 Exponential families 5.2 Transformation families 5.3 Problems 81 81 86 88 6 Sufficiency and completeness 6.1 Definitions and elementary properties 6.2 Completeness 6.3 The Lehmann-Scheffé Theorem 6.4 Estimation with convex loss functions 6.5 Problems 90 90 94 95 95 96 7 Two-sided tests and conditional inference 7.1 Two-sided hypotheses and two-sided tests 7.2 Conditional inference, ancillarity and similar tests 7.3 Confidence sets 7.4 Problems 98 99 105 114 117 8 Likelihood theory 8.1 Definitions and basic properties 8.2 The Cramér-Rao Lower Bound 8.3 Convergence of sequences of random variables 8.4 Asymptotic properties of maximum likelihood estimators 8.5 Likelihood ratio tests and Wilks’ Theorem 8.6 More on multiparameter problems 8.7 Problems 120 120 125 127 128 132 134 137 9 Higher-order theory 9.1 Preliminaries 9.2 Parameter orthogonality 9.3 Pseudo-likelihoods 9.4 Parametrisation invariance 9.5 Edgeworth expansion 9.6 Saddlepoint expansion 9.7 Laplace approximation of integrals 9.8 Thep* formula 9.9 Conditional inference in exponential families 9.10 Bartlett correction 9.11 Modified profile likelihood 9.12 Bayesian asymptotics 9.13 Problems 140 141 143 145 146 148 149 152 153 159 160 161 163 164 10 Predictive inference 10.1 Exact methods 10.2 Decision theory approaches 10.3 Methods based on predictive likelihood 10.4 Asymptotic methods 169 169 172 175 179
Contents 11 vii 10.5 Bootstrap methods 10.6 Conclusions and recommendations 10.7 Problems 183 185 186 Bootstrap methods 11.1 An inference problem 11.2 The prepivoting perspective 11.3 Data example: Bioequivalence 11.4 Further numerical illustrations 11.5 Conditional inference and the bootstrap 11.6 Problems 190 191 194 201 203 208 214 Bibliography Index 218 223
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| discipline | Mathematik Wirtschaftswissenschaften |
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| indexdate | 2024-07-10T00:05:41Z |
| institution | BVB |
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| language | English |
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| publisher | Cambridge Univ. Press |
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| series | Cambridge series in statistical and probabilistic mathematics |
| series2 | Cambridge series in statistical and probabilistic mathematics |
| spelling | Young, George Alastair Verfasser aut Essentials of statistical inference G. A. Young ; R. L. Smith 1. paperback ed. Cambridge [u.a.] Cambridge Univ. Press 2010 X, 225 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Cambridge series in statistical and probabilistic mathematics [16] Afleiding (logica) gtt Probabilités Statistique mathématique Statistische toetsen gtt Mathematical statistics Probabilities Statistische Schlussweise (DE-588)4182963-3 gnd rswk-swf Inferenzstatistik (DE-588)4247120-5 gnd rswk-swf Statistische Schlussweise (DE-588)4182963-3 s DE-604 Inferenzstatistik (DE-588)4247120-5 s b DE-604 Smith, Richard L. Verfasser aut Cambridge series in statistical and probabilistic mathematics [16] (DE-604)BV011442366 16 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024385917&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Young, George Alastair Smith, Richard L. Essentials of statistical inference Cambridge series in statistical and probabilistic mathematics Afleiding (logica) gtt Probabilités Statistique mathématique Statistische toetsen gtt Mathematical statistics Probabilities Statistische Schlussweise (DE-588)4182963-3 gnd Inferenzstatistik (DE-588)4247120-5 gnd |
| subject_GND | (DE-588)4182963-3 (DE-588)4247120-5 |
| title | Essentials of statistical inference |
| title_auth | Essentials of statistical inference |
| title_exact_search | Essentials of statistical inference |
| title_full | Essentials of statistical inference G. A. Young ; R. L. Smith |
| title_fullStr | Essentials of statistical inference G. A. Young ; R. L. Smith |
| title_full_unstemmed | Essentials of statistical inference G. A. Young ; R. L. Smith |
| title_short | Essentials of statistical inference |
| title_sort | essentials of statistical inference |
| topic | Afleiding (logica) gtt Probabilités Statistique mathématique Statistische toetsen gtt Mathematical statistics Probabilities Statistische Schlussweise (DE-588)4182963-3 gnd Inferenzstatistik (DE-588)4247120-5 gnd |
| topic_facet | Afleiding (logica) Probabilités Statistique mathématique Statistische toetsen Mathematical statistics Probabilities Statistische Schlussweise Inferenzstatistik |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=024385917&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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