  This paper proposes a spatial k-nearest neighbor method for nonparametric
prediction of real-valued spatial data and supervised classification for
categorical spatial data. The proposed method is based on a double nearest
neighbor rule which combines two kernels to control the distances between
observations and locations. It uses a random bandwidth in order to more
appropriately fit the distributions of the covariates. The almost complete
convergence with rate of the proposed predictor is established and the almost
sure convergence of the supervised classification rule was deduced. Finite
sample properties are given for two applications of the k-nearest neighbor
prediction and classification rule to the soil and the fisheries datasets
