A bivariate Gaussian-mixture family is given in which the MLE for the location parameter converges faster than the classical n to the power of minus one-half rate.
Kent, Michael Sorensen (1982)
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A Simple Bivariate Example of Fast Convergence Rates for Maximum Likelihood Estimates
A bivariate Gaussian-mixture family is given in which the MLE for the location parameter converges faster than the classical n to the power of minus one-half rate.