Rao-Blackwell Improvement - Quant Trader Interview Question
Difficulty: Hard
Category: Probability & Statistics
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Topics: Rao-Blackwell, sufficient statistic, estimator, variance reduction, conditional expectation
Problem Description
Suppose you're building a trading strategy and have an unbiased estimator $T$ for a parameter of interest (e.g., expected return of an asset). You also know a sufficient statistic $S$ for that same parameter. How can you use the Rao-Blackwell theorem to construct a potentially better estimator, and what properties does the resulting estimator possess?
Specifically, consider the estimator $ET | S$. What can you say about its bias and variance compared to the original estimator $T$?
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