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Smooth Discrimination Analysis
 Ann. Statist
, 1998
"... Discriminant analysis for two data sets in IR d with probability densities f and g can be based on the estimation of the set G = fx : f(x) g(x)g. We consider applications where it is appropriate to assume that the region G has a smooth boundary. In particular, this assumption makes sense if di ..."
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Discriminant analysis for two data sets in IR d with probability densities f and g can be based on the estimation of the set G = fx : f(x) g(x)g. We consider applications where it is appropriate to assume that the region G has a smooth boundary. In particular, this assumption makes sense if discriminant analysis is used as a data analytic tool. We discuss optimal rates for estimation of G. 1991 AMS: primary 62G05 , secondary 62G20 Keywords and phrases: discrimination analysis, minimax rates, Bayes risk Short title: Smooth discrimination analysis This research was supported by the Deutsche Forschungsgemeinschaft, Sonderforschungsbereich 373 "Quantifikation und Simulation okonomischer Prozesse", HumboldtUniversitat zu Berlin 1 Introduction Assume that one observes two independent samples X = (X 1 ; : : : ; X n ) and Y = (Y 1 ; : : : ; Ym ) of IR d valued i.i.d. observations with densities f or g, respectively. The densities f and g are unknown. An additional random variabl...