On Certain Finitely Generated Subgroups of Groups Which Split

Traditionally the neighbourhood size k in the k-nearest-neighbour algorithm is either fixed at the first nearest neighbour or is selected on the basis of a crossvalidation study. In this paper we present an alternative approach that develops the k-nearestneighbour algorithm using likelihood-based inference. Our method takes the form of a generalised linear regression on a set of knearest-neighbour autocovariates. By defining the k-nearest-neighbour algorithm in this way we are able to extend the method to accommodate the original predictor variables as possible linear effects as well as allowing for the inclusion of multiple nearestneighbour terms. The choice of the final model proceeds via a stepwise regression procedure. It is shown that our method incorporates a conventional generalised linear model and a conventional k-nearest-neighbour algorithm as special cases. Empirical results suggest that the method out-performs the standard k-nearest-neighbour method in terms of misclassification rate on a wide variety of datasets.