The Strong Consistency of the Conditional Probability of Error in Discrimination Based on Kernel Stereographic Projection Density Estimator

Let (X, Y), (X-1,Y-1), ... , (X-n, Y-n) be R-d x{1, ... , M} -valued i.i.d. random vectors, Z(n) = {(X-1, Y-1), ... (X-n, Y-n)}. (X, Y) is distribution free, to discriminate Y based on Z(n) and X belongs to nonparametric discrimination. Based on kernel stereographic projection density estimator (KSPDE), a new nonparametric discriminate rule is constructed. Under some weak conditions(see theorem 1), the exponential convergence rate and the strong consistency of the conditional probability of error in discrimination are obtained.