Properties of Conditional Expectation Operators and Sufficient Subfields

Details Properties of Conditional Expectation Operators and Sufficient Subfields Properties of Conditional Expectation Operators and Sufficient Subfields

2010-11-23

arxiv.org/abs/1011.5162v2

Mathematics

Statistics Theory

Scientific paper

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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