A Tree - Structured Approach to Nonparametric Multiple Regression

In the nonparametric regression problem, one is given a set of vector valued variables 3 (termed carriers) and with each an associated scalar quantity Y (termed the response). This set of carriers and associated responses CYi,Xil (l<i<N) is termed the training sample. In addition (usually at some later time), one is given another set of vector valued variables {Ljl (lsj<M) without corresponding responses and the problem is to estimate each corresponding response using the values of its carriers and the training sample. That is: