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Stochastic Limit TheoryAn Introduction for Econometricians$
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James Davidson

Print publication date: 1994

Print ISBN-13: 9780198774037

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0198774036.001.0001

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Conditioning

Conditioning

Chapter:
(p.143) 10 Conditioning
Source:
Stochastic Limit Theory
Author(s):

James Davidson

Publisher:
Oxford University Press
DOI:10.1093/0198774036.003.0010

This chapter deals in depth with the concept of conditional expectation. This is defined first in the traditional “naïve” manner, and then using the measure theoretic approach. A comprehensive set of properties of the conditional expectation are proved, generalizing several results of Ch. 9, and then multiple sub‐σ‐fields and nesting are considered, and a brief treatment of conditional distributions and conditional independence.

Keywords:   conditional distributions, conditional expectation, conditional independence, conditional inequalities, iterated expectations, nested sub‐σ‐fields, regular conditioning

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