Types of finite-sample consistency with the standard deviation

Let us say we have a robust dispersion estimator \(\operatorname{T}(X)\). If it is asymptotically consistent with the standard deviation, we can use such an estimator as a robust replacement for the standard deviation under normality. Thanks to asymptotical consistency, we can use the estimator “as is” for large samples. However, if the number of sample elements is small, we typically need finite-sample bias-correction factors to make the estimator unbiased. Here we should clearly understand wha...

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