Misclassification probability based on linear discriminant function for sar error models

Abstract

Given training sample, the problem of classifying Gaussian spatial data into one of two populations specified by spatial autoregressive model (SAR) with dif- ferent mean functions is considered. This paper concerns classification procedures associated with Linear Discriminant Function (LDF) under deterministic spatial sampling design. In the case of complete parametric certainty, the overall mis- classification probability associated with LDF is derived. Spatial weights based on inverse of Euclidean distance and the third order neighbourhood schemes on regular 2-dimensional lattice are used for illustrative examples. The effect of the prior distribution of class labels on the performance of proposed classification procedure is numerically evaluated.