Statistics

For graduate-level courses in Statistical Inference or Theoretical Statistics in departments of Statistics, Bio-Statistics, Economics, Computer Science, and Mathematics.

A classic, time-honored introduction to the theory and practice of statistics modeling and inference—revised to reflect the changing focus of Statistics and the mathematics background of today's students. 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. A second volume treating more advanced topics is in preparation.

• NEW - More rigorous, yet accessible.

  • Adds the necessary rigor for sophisticated masters- or doctoral-level work, yet keeps in mind the mathematics background that today's students bring to the course. Ex.___

• NEW - Unified Viewpoint—Views all models, parametric, semi-parametric, and non-parametric from a “coordinate free” point of view.

• NEW - More comprehensive coverage of key topics—E.g., multidimensional parameters, exponential families, algorithms (including EM), asymptotics and Bayesian methods.

  • Gives students a thorough understanding of statistical inference. Ex.___

• NEW - Computational issues discussed— Give a careful proof of the convergence of an algorithm (but the computer code is not supplied and there is no reference to standard statistical languages and packages).

• NEW - 50% more problems—Problems gradually increase in level from routine to more challenging. Some problems cover important ideas and results not treated in the text.

  • Helps students to gain confidence in their problem solving abilities. Ex.___

• Comprehensive, self-contained treatment of the various aspects of statistics—E.g., modeling, frequentist and Bayesian analysis (developed side by side), optimality, prediction, and large sample theory and methods. Appendices provided needed results from probability and analysis.

  • Helps students develop a thorough understanding of many aspects of statistical inference, and provides instructors with a comprehensive, single-source teaching tool. Ex.___

• Large number and variety of problems—Ranges from routine to challenging. Provides many hints for the difficult problems.

  • Gives beginning-level students the opportunity to develop their statistical skills systematically, one level at a time, without becoming frustrated and overwhelmed. Ex.___

• Theory related to conceptual and technical issues encountered in practice—Views theory as suggestive for practice, not prescriptive.

  • Shows students how assumptions which lead to neat theory may be unrealistic in practice. Ex.___

• More rigorous, yet accessible.

  • Adds the necessary rigor for sophisticated masters- or doctoral-level work, yet keeps in mind the mathematics background that today's students bring to the course. Ex.___

• Unified Viewpoint—Views all models, parametric, semi-parametric, and non-parametric from a “coordinate free” point of view.

• More comprehensive coverage of key topics—E.g., multidimensional parameters, exponential families, algorithms (including EM), asymptotics and Bayesian methods.

  • Gives students a thorough understanding of statistical inference. Ex.___

• Computational issues discussed— Give a careful proof of the convergence of an algorithm (but the computer code is not supplied and there is no reference to standard statistical languages and packages).

• 50% more problems—Problems gradually increase in level from routine to more challenging. Some problems cover important ideas and results not treated in the text.

  • Helps students to gain confidence in their problem solving abilities. Ex.___

(NOTE: Each chapter concludes with Problems and Complements, Notes, and References.)

1. Statistical Models, Goals, and Performance Criteria.

Mathematical Statistics (Statistics)

For graduate-level courses in Statistical Inference or Theoretical Statistics in departments of Statistics, Bio-Statistics, Economics, Computer Science, and Mathematics.


An updated printing! In response to feedback from faculty and students, some sections within the book have been rewritten. Also, a number of corrections have been made, further improving the accuracy of this outstanding textbook.




This updated 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.





KEY TOPICS: 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. 

• Mathematical Statistics, Updated Printing, 2/E
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  ISBN-10: 0132306379 | ISBN-13: 9780132306379
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Pearson Higher Education offers special pricing when you choose to package your text with other student resources. If you're interested in creating a cost-saving package for your students contact your Pearson Higher Education representative.