Data-dependent kn-NN and kernel estimators consistent for arbitrary processes

Let . . . be an arbitrary random process taking values in a totally bounded subset of a separable metric space. Associated with we observe drawn from an unknown conditional distribution ( = ) with continuous regression function ( ) = [ = ]. The problem of interest is to estimate based on and the data ( ) . We construct appropriate data-dependent nearest neighbor and kernel estimators and show, with a very elementary proof, that these are consistent for every process . . ..