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Probability pp 217-242 | Cite as

Prediction and Conditional Expectation

  • Alan F. Karr
Part of the Springer Texts in Statistics book series (STS)

Abstract

Let (Ω, F, P) be a probability space, and let L2 be the vector space of random variables Zwith E[Z2<∞. Let XL2 be an unobservable random variable, whose value we wish to predict from observation of other random variables Y1,..., Yn. (For example, Xmay be the value of a stochastic process at some time in the future, or a spatial process over a region where it cannot be observed). In order to use knowledge of Y1,..., Yn to predict X, the predictor must be function of Y1,..., Yn, and, in particular, is a random variable

Keywords

Mean Square Error Orthogonal Projection Conditional Distribution Conditional Expectation Minimum Mean Square Error 
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 Science+Business Media New York 1993

Authors and Affiliations

  • Alan F. Karr
    • 1
  1. 1.National Institute of Statistical SciencesUSA

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