Consistency of a nonparametric conditional mode estimator for random fields

摘要

Given a stationary multidimensional spatial process｛Z_i = (X_i, Y_i)∈R~d ×R,i∈Z~N｝, we investigate a kernel estimate of the spatial conditional mode function of the response variable Y_i given the explicative variable X_i. Consistency in L~P norm and strong convergence of the kernel estimate are obtained when the sample considered is a α-mixing sequence. An application to real data is given in order to illustrate the behavior of our methodology.