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Mathematical Statistics(2000)  무료배송

 
지은이 : Peter J. Bickel, Kjell A. Doksum
출판사 : Prentice Hall
판수 : 2nd edition
페이지수 : 556 pages
ISBN : 013850363x
예상출고일 : 입금확인후 2일 이내
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도서가격 : 품절
     

 

This classic, time-honored introduction to the theory and practice of statistics modeling and inference reflects the changing focus of contemporary Statistics. Coverage begins with the more general nonparametric point of view and then looks at parametric models as submodels of the nonparametric ones which can be described smoothly by Euclidean parameters. Although some computational issues are discussed, this is very much a book on theory. It relates theory to conceptual and technical issues encountered in practice, viewing theory as suggestive for practice, not prescriptive. It shows readers how assumptions which lead to neat theory may be unrealistic in practice. Statistical Models, Goals, and Performance Criteria. Methods of Estimation. Measures of Performance, Notions of Optimality, and Construction of Optimal Procedures in Simple Situations. Testing Statistical Hypotheses: Basic Theory. Asymptotic Approximations. Multiparameter Estimation, Testing and Confidence Regions. A Review of Basic Probability Theory. More Advanced Topics in Analysis and Probability. Matrix Algebra. For anyone interested in mathematical statistics working in statistics, bio-statistics, economics, computer science, and mathematics.

1. Statistical Models, Goals, and Performance Criteria.


Data, Models, Parameters, and Statistics. Bayesian Models. The Decision Theoretic Framework. Prediction. Sufficiency. Exponential Families.



2. Methods of Estimation.


Basic Heuristics of Estimation. Minimum Contrast Estimates and Estimating Equations. Maximum Likelihood in Multiparameter Exponential Families. Algorithmic Issues.



3. Measures of Performance.


Introduction. Bayes Procedures. Minimax Procedures. Unbiased Estimation and Risk Inequalities. Nondecision Theoretic Criteria.



4. Testing and Confidence Regions.


Introduction. Choosing a Test Statistic: The Neyman-Pearson Lemma. Uniformly Most Powerful Tests and Monotone Likelihood Ratio Models. Confidence Bounds, Intervals and Regions. The Duality between Confidence Regions and Tests. Uniformly Most Accurate Confidence Bounds. Frequentist and Bayesian Formulations. Prediction Intervals. Likelihood Ratio Procedures.



5. Asymptotic Approximations.


Introduction: The Meaning and Uses of Asymptotics. Consistency. First- and Higher-Order Asymptotics: The Delta Method with Applications. Asymptotic Theory in One Dimension. Asymptotic Behavior and Optimality of the Posterior Distribution.



6. Inference in the Multiparameter Case.


Inference for Gaussian Linear Models. Asymptotic Estimation Theory in p Dimensions. Large Sample Tests and Confidence Regions. Large Sample Methods for Discrete Data. Generalized Linear Models. Robustness Properties and Semiparametric Models.



Appendix A: A Review of Basic Probability Theory.


The Basic Model. Elementary Properties of Probability Models. Discrete Probability Models. Conditional Probability and Independence. Compound Experiments. Bernoulli and Multinomial Trials, Sampling with and without Replacement. Probabilities on Euclidean Space. Random Variables and Vectors: Transformations. Independence of Random Variables and Vectors. The Expectation of a Random Variable. Moments. Moment and Cumulant Generating Functions. Some Classical Discrete and Continuous Distributions. Modes of Convergence of Random Variables and Limit Theorems. Further Limit Theorems and Inequalities. Poisson Process.



Appendix B: Additional Topics in Probability and Analysis.


Conditioning by a Random Variable or Vector. Distribution Theory for Transformations of Random Vectors. Distribution Theory for Samples from a Normal Population. The Bivariate Normal Distribution. Moments of Random Vectors and Matrices. The Multivariate Normal Distribution. Convergence for Random Vectors: Op and Op Notation. Multivariate Calculus. Convexity and Inequalities. Topics in Matrix Theory and Elementary Hilbert Space Theory.



Appendix C: Tables.


The Standard Normal Distribution. Auxiliary Table of the Standard Normal Distribution. t Distribution Critical Values. X 2 Distribution Critical Values. F Distribution Critical Values.



Index.
"This is one of a number of good first year graduate texts on statistical theory. It was used at Berkeley for their students in the late 1970s and early 1980s. These authors put together many interesting and challenging exercises at the end of the chapters. However they did not provide solutions to any of the problems. When Marc Sobel was a graduate student, his father Milton, a statistics professor convinced Marc to work out every problem in the book! Marc did this and eventually he and Milton put together a solution manual which was published. In the process a number of mistakes were caught and corrected.
If you get the book try to get the solution manual as well. It will greatly deepen your understanding of the material and help you through the difficult problems.
My review pertains to the original book by Bickel and Doksum that was published in 1977 by Holden-Day. I was under the misimpression that Prentice-Hall was publishing a reprint of the old book due to its popularity and the non-existence of the original publisher. I was apparently mistaken as the title indicates Volume 1 of the Second Edition. This was pointed out to me by a reader.

In general if you have doubts check with the reviewer about the edition for books with multiple editions. Often reviewers write reviews for a particular edition and when the new edition comes out it accidentally gets moved. This can happen when amazon removes the page for the old edition because it no longer carries it. Reviews of old editions can still be helpful since the heart of the book usually remains the same and the quality of writing of the authors does not often change much. Of course a review of the new edition would be better if it has information on changes and additions and any particularly attractive new features of the book."


"Bickel and Doksum is of course a standard text in mathematical statistics. The development of the theory is thorough but not as complete as books by Lehmann or Cassella and Berger. I felt that Bickel and Doksum occasionally left out important theorems and details. Also, the examples given were sometimes unhelpful or irrelavent. I personally disliked their penchant for the hypergeometric distribution and Hardy-Weinberg equilibriums. Nevertheless, the writing is clear and the book gives a solid background of the fundamentals. Personally, I prefer Casella and Berger for a more complete overview."
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