Mathematical Statistics

Mathematical Statistics

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Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology. The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues. The result reaches beyond "nice" mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry.show more

Product details

  • Hardback | 504 pages
  • 157.48 x 231.14 x 33.02mm | 816.46g
  • Taylor & Francis Inc
  • Chapman & Hall/CRC
  • Boca Raton, FL, United States
  • English
  • 14 black & white tables
  • 158488178X
  • 9781584881780
  • 2,391,016

Review quote

Keith Knight's new book is a welcome addition to textbooks appropriate for masters-level theory courses. ... His is the best treatment of likelihood theory that I know at any level. ... I wish I had a nickel for every time I have been asked for recommended reading on likelihood theory and had to say one did not exist at this level. Now I can wholeheartedly recommend Mathematical Statistics. C. GEYER, University of Minnesota in Journal of the American Statistical Association, June 2001 "a very suitable text for teaching at an acceptable mathematical levelcontains numerous examples and each chapter is followed by a rich choice of exercisesthis makes the book excellent for teaching," -Short Book Reviews of the ISI "well-written, , , far greater coverage of ides that are not standard in other mathematical statistics texts." --M. S. Ridout, Institute of Mathematics and Statistics, University of Kent at Canterbury, UK in Biometrics "one of the five best textbooks on a beginning course on theoretical statistics providing a good grasp on the foundations of theoretical statistics. Primarily for graduate students with mathematical backgrounds in linear algebra, multivariable calculus, and some exposure to statistical methodology. Highly recommended for all academic libraries." --D. V. Chopra, Wichita State University in CHOICE "This books breaks away form more theoretically burdensome texts, focusing on providing a set of useful tools that help readers understand the theoretical under pinning of statistical methodology." --SciTech Book News, March 2000 "This (hardback) book is one of the most up-to-date and easily understood texts in the field of mathematical statistics. The author has recognizedthe difficult nature of the subject and has done justice to the subject by finally producing one of the best well-rounded texts for graduate and senior undergraduate students. well written and well structured. This text would be a very useful teaching tool." The Statistician, Vol. 50, Part 2, 2001show more

Table of contents

INTRODUCTION TO PROBABILITY Random Experiments Probability Measures Conditional Probability and Independence Random Variables Expected Values RANDOM VECTORS AND JOINT DISTRIBUTIONS Introduction Discrete and Continuous Random Vectors Conditional Distributions Normal Distributions Poisson Processes Generating Random Variables CONVERGENCE OF RANDOM VARIABLES Introduction Convergence in Probability and Distribution WLLN Proving Convergence in Distribution CLT Some Applications Convergence with Probability 1 PRINCIPLES OF POINT ESTIMATION Introduction Statistical Models Sufficiency Point Estimation Substitution Principle Influence Curves Standard Errors Relative Efficiency The Jackknife LIKELIHOOD-BASED ESTIMATION Introduction The Likelihood Function The Likelihood Principle Asymptotics for MLEs Misspecified Models Nonparametric Maximum Likelihood Estimation Numerical Computation Bayesian Estimation OPTIMAL ESTIMATION Decision Theory UMVUEs The Cramer-Rao Lower Bound Asymptotic Efficiency INTERVAL ESTIMATION AND HYPOTHESIS TESTING Confidence Intervals and Regions Highest Posterior Density Regions Hypothesis Testing Likelihood Ratio Tests Other Issues LINEAR AND GENERALIZED LINEAR MODELS Linear Models Estimation Testing Non-Normal Errors Generalized Linear Models Quasi-Likelihood Models GOODNESS OF FIT Introduction Tests Based on the Multinomial Distribution Smooth Goodness of Fit Tests REFERENCES Each chapter also contains a Problems and Complements sectionshow more

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