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. Features1.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. 2. Unified Viewpoint　　Views all models, parametric, semi-parametric, and non-parametric from a “coordinate free” point of view.3.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. 4.Computational issues discussed　　Give a careful proof of the convergence of an algorithm.5.50% more problems　　Problems gradually increase in level from routine to more challenging. Some problems cover important ideas and results not treated in the text. 6.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. 7.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. 8.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.

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