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

摘要

Let (X,Y), (X_1,Y_1),…,(X_n,Y_m) be R~d×{1,…,M} -valued i.i.d. random vectors, Z_n={(X_1,Y_1),…(X_n,Y_ri)}.(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.