Almost everywhere convergence of a recursive regression function estimate and classification (Corresp.)

It is shown that the recursive kernel estimate of the regression function
E(Y|X = x)
is consistent at almost every
x(\mu)
regardless of the distribution
\mu
of
X
. Thus the result is distribution-free. From this we show that the risk for a suitable classification rule derived from the estimate converges to Bayes' risk, no matter what the class distributions are.