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  3. Comparison of Statistical Experiments
  • Cited by 137
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    • Publisher:
      Cambridge University Press
      Publication date:
      05 May 2013
      14 March 1991
      ISBN:
      9780511666353
      9780521250306
      9780521102827
      DOI:
      https://doi.org/10.1017/CBO9780511666353
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      1.236kg, 696 Pages
      Dimensions:
      (234 x 156 mm)
      Weight & Pages:
      0.96kg, 696 Pages
      • Subjects:
      Mathematics (general), Mathematics, Abstract Analysis, Statistical Theory and Methods, Statistics and Probability
      Series:
      Encyclopedia of Mathematics and its Applications (36)
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    Subjects:
    Mathematics (general), Mathematics, Abstract Analysis, Statistical Theory and Methods, Statistics and Probability
    Series:
    Encyclopedia of Mathematics and its Applications (36)
    Information

    Book description

    There are a number of important questions associated with statistical experiments: when does one given experiment yield more information than another; how can we measure the difference in information; how fast does information accumulate by repeating the experiment? The means of answering such questions has emerged from the work of Wald, Blackwell, LeCam and others and is based on the ideas of risk and deficiency. The present work which is devoted to the various methods of comparing statistical experiments, is essentially self-contained, requiring only some background in measure theory and functional analysis. Chapters introducing statistical experiments and the necessary convex analysis begin the book and are followed by others on game theory, decision theory and vector lattices. The notion of deficiency, which measures the difference in information between two experiments, is then introduced. The relation between it and other concepts, such as sufficiency, randomisation, distance, ordering, equivalence, completeness and convergence are explored. This is a comprehensive treatment of the subject and will be an essential reference for mathematical statisticians.

    Reviews

    "The book may serve as a textbook for the mathematical background of statistics, but it is also of great importance for research. Hopefully, the monograph will inspire many statisticians to apply the methods presented also in practical problems." Arnold Janssen, Mathematical Reviews

    "...impressive volume....It is very rich in content and replete with examples....quite self contained and fairly easy to read." Lucin Le Cam, SIAM Review

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