Measuring performance of robust estimator for the variance of generalized Gaussian distribution

摘要

We consider the calculating performance of a robust estimator for the variance of a generalized Gaussian distribution. In detail, we apply an unbiased ML estimator and a robust estimator for the variance of a Gaussian distribution to the variance of a generalized Gaussian distribution and calculate the mean square error. Then, we determine how the performance (= inverted MSE) changes as the actual distribution varies over this generalized Gaussian distribution which represents a Gaussian, Laplace, or Cauchy distribution. Results indicate that, for robustness, heavy censoring (small k) should be employed for a small number of samples, while less censoring (large k) can be appropriate for a large number of samples.