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Hard · Probability & Statistics · Quant Trader interview question · probability, statistics, estimation, cramer-rao-lower-bound, fisher-information
Suppose you are trying to estimate a parameter $ \theta $ using an unbiased estimator $ \hat{\theta} $ based on $ n $ independent and identically distributed (i.i.d.) observations from a distribution with probability density function (PDF) $ f(x; \theta) $. What is the fundamental lower bound on the variance of any such unbiased estimator?