Covariance Estimation for cauchy noise

Question

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?

Answer 1

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.