Properties of Conditional Expectation Operators and Sufficient Subfields
classification
🧮 math.ST
stat.TH
keywords
sufficientconditionalexpectationoperatorspropertiesburkholderchowcomplete
read the original 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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