Cramer_Rao_inequality

introduction

%%visits: 5 ## intuition The Cramer_Rao_inequality motivates the idea of [[efficiency]]. ## rigour Theorem- Let X₁, …, X_n be i.i.d.s with probability density function f(x;0). Let θ̂_n be an unbiased estimator of θ. Then under “mild” conditions.

Mild is defined as when supp(g(x)) is independent of θ then $$ var(\hat{\theta}_n) \ge \frac{1}{In(\theta)} $$ Recall that I_n(θ) is the [[Fisher_information]] ## exam clinic ## resources tags :math:probability_and_statistics_2:

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