Comparison of a distance-based likelihood ratio test and k-nearest neighbor classification methods

Several studies of the k-nearest neighbor (KNN) classifier have proposed the use of non-uniform weighting on the k neighbors. It has been suggested that the distance to each neighbor can be used to calculate the individual weights in a weighted KNN approach; however, a consensus has not yet been reached on the best method or framework for calculating weights using the distances. In this paper, a distance likelihood ratio test will be discussed and evaluated using simulated data. The distance likelihood ratio test (DLRT) shares several characteristics with the distance-weighted k-nearest neighbor methods but approaches the use of distance from a different perspective. Results illustrate the ability of the distance likelihood ratio test to approximate the likelihood ratio and compare the DLRT to two other k-neighborhood classification rules that utilize distance-weigbting. The DLRT performs favorably in comparisons of the classification performance using the simulated data and provides an alternative non-parametric classification method for consideration when designing a distance-weighted KNN classification rule.