A general approach to classification problems (Q1069623)

In the classification problem the value of the discrete random variable I must be estimated from that of a random variable X given a random sample \((I_ 1,X_ 1)\), \((I_ 2,X_ 2),...,(I_ n,X_ n)\). A classification rule giving such an estimate can be based on most nonparametric density estimators which are based on delta sequences. The rate at which the nonerror rate for this rule converges to the optimal is calculated. It is found to be \(O(n^{-1/(2d+2)}\log^ dn\), where d is the dimension of the variable X under mild assumptions on the densities. A procedure for choosing an associated parameter for small samples is given.