The authors consider the nonparametric regression model
, where g is a bounded function over the interval [0,1] which is to be estimated,
are nonrandom and
are independent identically distributed random variables with
. They study the behavior of the general family of nonparametric estimates
, where the weight functions
are of the form
. Sufficient conditions for mean square and complete convergence are derived. Also proposed is a class of new nearest neighbor estimates of g. A simulation experiment demonstrates the success of the nearest neighbor technique with bandwidth depending on the local density of the design points.