Ingo Steinke
Asymptotic optimal classification of three populations by ML-estimators
The paper is published: Rostocker Mathematische Kolloquium, Rostock. Math. Kolloq. 49, 31-43 (1995)
62F05 Asymptotic properties of tests
62F12 Asymptotic properties of estimators
Abstract: Let \pi_1 and \pi_2 be independent populations distributed according to
Q_{\theta_1} and Q_{\theta_2} with unknown parameters \theta_1, \theta_2
\in H and let \pi_3 be a third population whose distribution Q_{\theta_3}
coincides with that of either \pi_1 or \pi_2. Assume there are given
samples of size n_1=n_2 and n_3, it is not to be decided whether
Q_{\theta_3}=Q_{\theta_1} or Q_{\theta_3}=Q_{\theta_2}. The desicion
problem is described by a sequence of localized experiments. The
corresponding lower Hajek-LeCam-bound is established and there is
constructed a sequence of decision rules based on ML-estimators which
attains this bound and is therefore considered to be asymptotic optimal.
Keywords: classification of 3 populations, Hajek-LeCam bound, weakly convergent experiments