Invariant estimator: Difference between revisions

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If <math>x \sim N(\theta 1_n,I)\,\!</math> (i.e. a [[multivariate normal distribution]] with independent, unit-variance components) then
:<math>\delta_{pitman\text{Pitman}} = \delta_{ML}=\frac{\sum{x_i}}{n}.</math>
 
If <math>x \sim C(\theta 1_n,I \sigma^2)\,\!</math> (independent components having a [[Cauchy distribution]] with scale parameter ''&sigma;'') then