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Apart from Ledoit wolf shrinkage technique which can be better shrinkage covariance estimators for data with cauchy distribution? How to calculate optimum shrinkage intensity for data containing cauchy distribution? I have gone through many shrinkage covariance estimators dealing with normal data or exponential distributions but didnt get for cauchy distribution can anyone suggest?

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That's probably because the Cauchy distribution does not have finite variance, so it would not make sense to estimate variance-covariance in the first place. See the Wikipedia page for the Cauchy distribution or google "Cauchy distribution variance" for more information.

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