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Ancillary Statistics, Pivotal Quantities and Confidence Statements

  • J. K. Ghosh
Part of the Lecture Notes in Statistics book series (LNS, volume 45)

Abstract

The most commonly used expression in Statistics is information; yet, we have no agreement on the definition or usage of this concept. However, in the particular situation where the problem is to predict a future value of a random variable X with a known probability distribution p(.), we all seem to agree that the information on the yet unobserved future value of X may be characterized by the function p(.) itself. And if we have another variable Y such that the conditional distribution p(.|Y) of X, given Y, is also known then, having observed Y, we can claim that the information on X has shifted from p(.) to p(.| Y). [To avoid a multiplicity of notations, we do not distinguish between a random variable X, an observed value of X and a typical point in the sample space of X.] If p(.|Y) is the same for all values of Y, then X is stochastically independent of Y. In this case Y is said to have no information on X. And we know how to prove then that X has no information on Y.

Keywords

Likelihood Function Conditional Distribution Sample Space Confidence Statement Fair Coin 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • J. K. Ghosh
    • 1
  1. 1.Indian Statistical InstituteCalcuttaIndia

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