# Theory of Statistics

## Schervish, Mark J.

Valutazione media 3,5
( su 2 valutazioni fornite da GoodReads )

The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. An important strength of this book is that it provides a mathematically rigorous and even-handed account of both Classical and Bayesian inference in order to give readers a broad perspective. For example, the "uniformly most powerful" approach to testing is contrasted with available decision-theoretic approaches.

Le informazioni nella sezione "Riassunto" possono far riferimento a edizioni diverse di questo titolo.

Recensione:

From the reviews:

"Another excellent book in theory of statistics is by Mark J. Schervish. … Readers will enjoy reading this book to see how differently the theory can be presented … . This well written book contains nine chapters and four appendices. ... Each chapter has both easy and challenging problems. The book is suitable for graduate level statistical theory courses. Examples and illustrations are well explained. I liked the author’s presentation, and learned a lot from the book. I highly recommend this book to theoretical statisticians." (Ramalingam Shanmugam, Journal of Statistical Computation and Simulation, Vol. 74 (11), November, 2004)

Contenuti:

Content.- 1: Probability Models.- 1.1 Background.- 1.1.1 General Concepts.- 1.1.2 Classical Statistics.- 1.1.3 Bayesian Statistics.- 1.2 Exchangeability.- 1.2.1 Distributional Symmetry.- 1.2.2 Frequency arid Exchangeability.- 1.3 Parametric Models.- 1.3.1 Prior, Posterior, and Predictive Distributions.- 1.3.2 Improper Prior Distributions.- 1.3.3 Choosing Probability Distributions.- 1.4 DeFinetti’s Representation Theorem.- 1.4.1 Understanding the Theorems.- 1.4.2 The Mathematical Statements.- 1.4.3 Some Examples.- 1.5 Proofs of DeFinetti’s Theorem and Related Results*.- 1.5.1 Strong Law of Large Numbers.- 1.5.2 The Bernoulli Case.- 1.5.3 The General Finite Case*.- 1.5.4 The General Infinite Case.- 1.5.5 Formal Introduction to Parametric Models*.- 1.6 Infinite-Dimensional Parameters*.- 1.6.1 Dirichlet Processes.- 1.6.2 Tailfree Processes+.- 1.7 Problems.- 2: Sufficient Statistics.- 2.1 Definitions.- 2.1.1 Notational Overview.- 2.1.2 Sufficiency.- 2.1.3 Minimal and Complete Sufficiency.- 2.1.4 Ancillarity.- 2.2 Exponential Families of Distributions.- 2.2.1 Basic Properties.- 2.2.2 Smoothness Properties.- 2.2.3 A Characterization Theorem*.- 2.3 Information.- 2.3.1 Fisher Information.- 2.3.2 Kullback-Leibler Information.- 2.3.3 Conditional Information*.- 2.3.4 Jeffreys’ Prior*.- 2.4 Extremal Families*.- 2.4.1 The Main Results.- 2.4.2 Examples.- 2.4.3 Proofs+.- 2.5 Problems.- Chapte 3: Decision Theory.- 3.1 Decision Problems.- 3.1.1 Framework.- 3.1.2 Elements of Bayesian Decision Theory.- 3.1.3 Elements of Classical Decision Theory.- 3.1.4 Summary.- 3.2 Classical Decision Theory.- 3.2.1 The Role of Sufficient Statistics.- 3.2.2 Admissibility.- 3.2.3 James—Stein Estimators.- 3.2.4 Minimax Rules.- 3.2.5 Complete Classes.- 3.3 Axiomatic Derivation of Decision Theory*.- 3.3.1 Definitions and Axioms.- 3.2.2 Examples.- 3.3.3 The Main Theorems.- 3.3.4 Relation to Decision Theory.- 3.3.5 Proofs of the Main Theorems*.- 3.3.6 State-Dependent Utility*.- 3.4 Problems.- 4: Hypothesis Testing.- 4.1 Introduction.- 4.1.1 A Special Kind of Decision Problem.- 4.1.2 Pure Significance Tests.- 4.2 Bayesian Solutions.- 4.2.1 Testing in General.- 4.2.2 Bayes Factors.- 4.3 Most Powerful Tests.- 4.3.1 Simple Hypotheses and Alternatives.- 4.3.2 Simple Hypotheses, Composite Alternatives.- 4.3.3 One-Sided Tests.- 4.3.4 Two-Sided Hypotheses.- 4.4 Unbiased Tests.- 4.4.1 General Results.- 4.4.2 Interval Hypotheses.- 4.4.3 Point Hypotheses.- 4.5 Nuisance Parameters.- 4.5.1 Neyinan Structure.- 4.5.2 Tests about Natural Parameters.- 4.5.3 Linear Combinations of Natural Parameters.- 4.5.4 Other Two-Sided Cases*.- 4.5.5 Likelihood Ratio Tests.- 4.5.6 The Standard F-Test as a Bayes Rule.- 4.6 P-Values.- 4.6.1 Definitions and Examples.- 4.6.2 P-Values and Bayes Factors.- 4.7 Problems.- 5: Estimation.- 5.1 Point Estimation.- 5.1.1 Minimum Variance Unbiased Estimation.- 5.1.2 Lower Bounds on the Variance of Unbiased Estimators.- 5.1.3 Maximum Likelihood Estimation.- 5.1.4 Bayesian Estimation.- 5.1.5 Robust Estimation*.- 5.2 Set Estimation.- 5.2.1 Confidence Sets.- 5.2.2 Prediction Sets*.- 5.2.3 Tolerance Sets*.- 5.2.4 Bayesian Set Estimation.- 5.2.5 Decision Theoretic Set Estimation.- 5.3 The Bootstrap*.- 5.3.1 The General Concept.- 5.3.2 Standard Deviations and Bias.- 5.3.3 Bootstrap Confidence Intervals.- 5.4 Problems.- 6: Equivariance*.- 6.1 Common Examples.- 6.1.1 Location Problems.- 6.1.2 Scale Problems.- 6.2 Equivariant Decision Theory.- 6.2.1 Groups of Transformations.- 6.2.2 Equivariance and Changes of Units.- 6.2.3 Minimum Risk Equivariant Decisions.- 6.3 Testing and Confidence Intervals*.- 6.3.1 P-Values in Invariant Problems.- 6.3.2 Equivariant Confidence Sets.- 6.3.3 Invariant Tests*.- 6.4 Problems.- 7: Large Sample Theory.- 7.1 Convergence Concepts.- 7.1.1 Deterministic Convergence.- 7.1.2 Stochastic Convergence.- 7.1.3 The Delta Method.- 7.2 Sample Quantiles.- 7.2.1 A Single Quantile.- 7.2.2 Several Quantiles.- 7.2.3 Linear Combinations of Quantiles*.- 7.3 Large Sample Estimation.- 7.3.1 Some Principles of Large Sample Estimation.- 7.3.2 Maximum Likelihood Estimators.- 7.3.3 MLEs in Exponential Families.- 7.3.4 Examples of Inconsistent MLEs.- 7.3.5 Asymptotic Normality of MLEs.- 7.3.6 Asymptotic Properties of M-Estimators.- 7.4 Large Sample Properties of Posterior Distributions.- 7.4.1 Consistency of Posterior Distributions+.- 7.4.2 Asymptotic Normality of Posterior Distributions.- 7.4.3 Laplace Approximations to Posterior Distributions*.- 7.4.4 Asymptotic Agreement of Predictive Distributions+.- 7.5 Large Sample Tests.- 7.5.1 Likelihood Ratio Tests.- 7.5.2 Chi-Squarcd Goodness of Fit Tests.- 7.6 Problems.- 8: Hierarchical Models.- 8.1 Introduction.- 8.1.1 General Hierarchical Models.- 8.1.2 Partial Exchangeability*.- 8.1.3 Examples of the Representation Theorem*.- 8.2 Normal Linear Models.- 8.2.1 One-Way ANOVA.- 8.2.2 Two-Way Mixed Model ANOVA*.- 8.2.3 Hypothesis Testing.- 8.3 Nonnormal Models*.- 8.3.1 Poisson Process Data.- 8.3.2 Bernoulli Process Data.- 8.4 Empirical Bayes Analysis*.- 8.4.1 Naïve Empirical Bayes.- 8.4.2 Adjusted Empirical Bayes.- 8.4.3 Unequal Variance Case.- 8.5 Successive Substitution Sampling.- 8.5.1 The General Algorithm.- 8.5.2 Normal Hierarchical Models.- 8.5.3 Nonnormal Models.- 8.6 Mixtures of Models.- 8.6.1 General Mixture Models.- 8.6.2 Outliers.- 8.6.3 Bayesian Robustness.- 8.7 Problems.- 9: Sequential Analysis.- 9.1 Sequential Decision Problems.- 9.2 The Sequential Probability Ratio Test.- 9.3 Interval Estimation*.- 9.4 The Relevancc of Stopping Rules.- 9.5 Problems.- Appendix A: Measure and Integration Theory.- A.1 Overview.- A.1.1 Definitions.- A.1.2 Measurable Functions.- A.1.3 Integration.- A.1.4 Absolute Continuity.- A.2 Measures.- A.3 Measurable Functions.- A.4 Integration.- A.5 Product Spaces.- A.6 Absolute Continuity.- A.7 Problems.- Appendix B: Probability Theory.- B.1 Overview.- B.1.1 Mathematical Probability.- B.1.2 Conditioning.- B.1.3 Limit Theorems.- B.2 Mathematical Probability.- B.2.1 Random Quantities and Distributions.- B.2.2 Some Useful Inequalities.- B.3 Conditioning.- B.3.1 Conditional Expectations.- B.3.2 Borel Spaces*.- B.3.3 Conditional Densities.- B.3.4 Conditional Independence.- B.3.5 The Law of Total Probability.- B.4 Limit Theorems.- B.4.1 Convergence in Distribution and in Probability.- B.4.2 Characteristic Functions.- B.5 Stochastic Processes.- B.5.1 Introduction.- B.5.3 Markov Chains*.- B.5.4 General Stochastic Processes.- B.6 Subjective Probability.- B.7 Simulation*.- B.8 Problems.- Appendix C: Mathematical Theorems Not Proven Here.- C.1 Real Analysis.- C.2 Complex Analysis.- C.3 Functional Analysis.- Appendix D: Summary of Distributions.- D.1 Univariate Continuous Distributions.- D.2 Univariate Discrete Distributions.- D.3 Multivariate Distributions.- References.- Notation and Abbreviation Index.- Name Index.

Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.

Compra nuovo Guarda l'articolo
EUR 102,67

Spese di spedizione: EUR 4,95
Da: Germania a: Italia

Destinazione, tempi e costi

Aggiungere al carrello

## 1.Theory of Statistics

Editore: Springer Dez 1996 (1996)
ISBN 10: 0387945466 ISBN 13: 9780387945460
Nuovi Quantità: 1
Valutazione libreria

Descrizione libro Springer Dez 1996, 1996. Buch. Condizione libro: Neu. 235x155x44 mm. Neuware - The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. 724 pp. Englisch. Codice libro della libreria 9780387945460

Compra nuovo
EUR 102,67
Convertire valuta
Spese di spedizione: EUR 4,95
Da: Germania a: Italia
Destinazione, tempi e costi

## 2.Theory of Statistics

Editore: Springer Dez 1996 (1996)
ISBN 10: 0387945466 ISBN 13: 9780387945460
Nuovi Quantità: 1
Da
AHA-BUCH GmbH
(Einbeck, Germania)
Valutazione libreria

Descrizione libro Springer Dez 1996, 1996. Buch. Condizione libro: Neu. 235x155x44 mm. Neuware - The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. 724 pp. Englisch. Codice libro della libreria 9780387945460

Compra nuovo
EUR 102,67
Convertire valuta
Spese di spedizione: EUR 8,90
Da: Germania a: Italia
Destinazione, tempi e costi

## 3.Theory of Statistics

Editore: Springer Dez 1996 (1996)
ISBN 10: 0387945466 ISBN 13: 9780387945460
Nuovi Quantità: 1
Da
Rheinberg-Buch
Valutazione libreria

Descrizione libro Springer Dez 1996, 1996. Buch. Condizione libro: Neu. 235x155x44 mm. Neuware - The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. 724 pp. Englisch. Codice libro della libreria 9780387945460

Compra nuovo
EUR 102,67
Convertire valuta
Spese di spedizione: EUR 9,89
Da: Germania a: Italia
Destinazione, tempi e costi

## 4.Theory of Statistics

Editore: Springer Dez 1996 (1996)
ISBN 10: 0387945466 ISBN 13: 9780387945460
Nuovi Quantità: 1
Da
Agrios-Buch
Valutazione libreria

Descrizione libro Springer Dez 1996, 1996. Buch. Condizione libro: Neu. 235x155x44 mm. Neuware - The aim of this graduate textbook is to provide a comprehensive advanced course in the theory of statistics covering those topics in estimation, testing, and large sample theory which a graduate student might typically need to learn as preparation for work on a Ph.D. 724 pp. Englisch. Codice libro della libreria 9780387945460

Compra nuovo
EUR 102,67
Convertire valuta
Spese di spedizione: EUR 9,90
Da: Germania a: Italia
Destinazione, tempi e costi

## 5.Theory of Statistics (Springer Series in Statistics)

Editore: Springer (1996)
ISBN 10: 0387945466 ISBN 13: 9780387945460
Nuovi Rilegato Quantità: 1
Da
Valutazione libreria

Descrizione libro Springer, 1996. Condizione libro: New. Codice libro della libreria UA9780387945460

Compra nuovo
EUR 102,67
Convertire valuta
Spese di spedizione: EUR 9,99
Da: Germania a: Italia
Destinazione, tempi e costi

## 6.Theory of Statistics

Editore: Springer (1995)
ISBN 10: 0387945466 ISBN 13: 9780387945460
Nuovi Rilegato Quantità: 1
Da
Herb Tandree Philosophy Books
(Stroud, GLOS, Regno Unito)
Valutazione libreria

Descrizione libro Springer, 1995. Hardback. Condizione libro: NEW. 9780387945460 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. Codice libro della libreria HTANDREE0275478

Compra nuovo
EUR 105,12
Convertire valuta
Spese di spedizione: EUR 9,49
Da: Regno Unito a: Italia
Destinazione, tempi e costi

## 7.Theory of Statistics (Springer Series in Statistics)

Editore: Springer (1995)
ISBN 10: 0387945466 ISBN 13: 9780387945460
Nuovi Rilegato Quantità: 1
Da
Revaluation Books
(Exeter, Regno Unito)
Valutazione libreria

Descrizione libro Springer, 1995. Hardcover. Condizione libro: Brand New. 702 pages. 9.75x6.50x1.75 inches. In Stock. Codice libro della libreria __0387945466

Compra nuovo
EUR 102,98
Convertire valuta
Spese di spedizione: EUR 17,80
Da: Regno Unito a: Italia
Destinazione, tempi e costi

## 8.Theory of Statistics

Editore: Springer-Verlag New York Inc. (1996)
ISBN 10: 0387945466 ISBN 13: 9780387945460
Nuovi Quantità: > 20
Print on Demand
Da
PBShop
(Wood Dale, IL, U.S.A.)
Valutazione libreria

Descrizione libro Springer-Verlag New York Inc., 1996. HRD. Condizione libro: New. New Book.Shipped from US within 10 to 14 business days.THIS BOOK IS PRINTED ON DEMAND. Established seller since 2000. Codice libro della libreria IP-9780387945460

Compra nuovo
EUR 112,35
Convertire valuta
Spese di spedizione: EUR 10,58
Da: U.S.A. a: Italia
Destinazione, tempi e costi

## 9.Theory of Statistics

Editore: Springer (2016)
ISBN 10: 0387945466 ISBN 13: 9780387945460
Nuovi Paperback Quantità: 1
Print on Demand
Da
Ria Christie Collections
(Uxbridge, Regno Unito)
Valutazione libreria

Descrizione libro Springer, 2016. Paperback. Condizione libro: New. PRINT ON DEMAND Book; New; Publication Year 2016; Not Signed; Fast Shipping from the UK. No. book. Codice libro della libreria ria9780387945460_lsuk

Compra nuovo
EUR 117,73
Convertire valuta
Spese di spedizione: EUR 5,30
Da: Regno Unito a: Italia
Destinazione, tempi e costi

## 10.Theory of Statistics

Editore: Springer-Verlag New York Inc. (1996)
ISBN 10: 0387945466 ISBN 13: 9780387945460
Nuovi Quantità: > 20
Print on Demand
Da
Books2Anywhere
(Fairford, GLOS, Regno Unito)
Valutazione libreria

Descrizione libro Springer-Verlag New York Inc., 1996. HRD. Condizione libro: New. New Book. Delivered from our US warehouse in 10 to 14 business days. THIS BOOK IS PRINTED ON DEMAND.Established seller since 2000. Codice libro della libreria IP-9780387945460

Compra nuovo
EUR 111,44
Convertire valuta
Spese di spedizione: EUR 11,87
Da: Regno Unito a: Italia
Destinazione, tempi e costi