On the existence of strongly consistent rules for estimation and classification
Sanjeev R. Kulkarni, Ofer Zeitouni · 2002
Suppose we observe x/sub 1/,x/sub 2/,.../spl epsiv//spl Xscr/ drawn i.i.d. according to some unknown distribution P selected from a family of distributions /spl Pscr/. Let f:/spl Pscr//spl rarr//spl Lambda/ be a parameterisation of P/spl isin//spl Pscr/. In this paper, we study necessary and sufficient conditions for the existence of strongly consistent estimators of f(P). A number of previous results along these lines are special cases of our main result.