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Competitive Stats
Q45Section I (Objective (Q1–Q80))45 of 80

Non-existence of an MVB estimator — Cauchy

Let x1,x2,…,xnx_1,x_2,\dots,x_n be a random sample from a distribution with probability density function

f(x;θ)=1π⋅11+(x−θ)2;−∞<x<∞,θ is real.f(x;\theta)=\frac1\pi\cdot\frac1{1+(x-\theta)^2};\qquad -\infty<x<\infty, \theta\text{ is real.}

Then the minimum variance bound estimator of θ\theta:

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