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In this paper we present a unified approach to obtaining rates of convergence for the maximum likelihood estimator (MLE) in Brownian semimartingale models of the form dX t ¼  n,Ł t dt þ  n t dWt, t < Tn: We show that the rate of the MLE is determined by (an appropriate version of) the entropy of the parameter space with respect to the random metric hn, defined by h 2 n(Ł, l) ¼ ð Tn 0  n,Ł s   n,l s  n  2 ds: Several known results for the rates in certain popular sub-models of the Brownian semimartingale model are shown to be special cases in our general framework.

On the rate of convergence of the maximum likelihood estimator in Brownian semimartingale models