Cramér-Rao Lower Bound - Quant Trader Interview Question
Difficulty: Hard
Category: Probability & Statistics
Practice quant interview questions from top firms including Jane Street, Citadel, Two Sigma, DE Shaw, and other leading quantitative finance companies.
Topics: probability, statistics, estimation, cramer-rao-lower-bound, fisher-information
Problem Description
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?
Practice this hard trader interview question on MyntBit - the all-in-one quant learning platform with 200+ quant interview questions for Jane Street, Citadel, Two Sigma, and other top quantitative finance firms.