Properties of Conditional Expectation Operators and Sufficient Subfields

Andrew Tausz

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arXiv · 1011.5162

Properties of Conditional Expectation Operators and Sufficient Subfields

Andrew Tausz

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Abstract

We discuss some properties of conditional expectation operators, and use these facts to prove an interesting counterexample regarding sufficient statistics. In particular, we show that there exists sufficient random variables X and Y, such that (X, Y) are jointly not sufficient. We follow the work of Burkholder and Chow, presenting complete proofs and supplying missing steps.

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Andrew Tausz. 2010-11-23. Properties of Conditional Expectation Operators and Sufficient Subfields. https://arxiv.org/abs/1011.5162

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