Ingo Steinke
Asymptotic optimal classification of three populations by ML-estimators
Preprint series: Preprints aus dem Fachbereich Mathematik, Universität Rostock
MSC:
62F05 Asymptotic properties of tests
62F12 Asymptotic properties of estimators
Abstract: Let $\pi_1$ and $\pi_2$ be independent populations distributed
according to $Q_{\vartheta_1}$ and $Q_{\vartheta_2}$ with
unknown parameters $\vartheta_1,\, \vartheta_2\in \cal H$
and let $\pi_3$ be a third population whose distribution
$Q_{\vartheta_3}$ 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 to be decided whether
$Q_{\vartheta_3}=Q_{\vartheta_1}$ or
$Q_{\vartheta_3}=Q_{\vartheta_2}$.\par
The decision 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 populations, Hajek-LeCam-bound