Counter-examples in Probability and Statistics

Counter-examples in Probability and Statistics

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Romano and Siegel have provided a collection of counter-examples from which students, teachers and researchers may benefit, as well as several approaches to the process of deciding a conjecture. Each chapter begins with an introduction, including pertinent definitions and results for that subject area. The chapters are ordered according to difficulty, from basic material to refinements and more specialized areas. This book should be of interest to undergraduate and graduate students on courses in statistics; professional statisticians.
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Product details

  • Hardback | 350 pages
  • Kluwer Academic Publishers
  • Dordrecht, Netherlands
  • 0534055680
  • 9780534055684

Table of contents

Probability spaces. Random variables, densities and distribution functions. Moments of random variables. Properties of real random variables. Sequences of random variables. Conditional expectation, Martingales, and almost sure convergence of sums of independent random variables. Properties of statistical experiments. Construction of estimators. Optimality of estimators. Confidence intervals and hypothesis testing. Appendix: Additional counter-examples.
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