The influence of training sampling size on the expected error rate in spatial classification

Abstract

In this paper we use the pluged-in Bayes discriminant function (PBDF) for classification of spatial Gaussian data into one of two populations specified by different parametric mean models and common geometric anisotropic covariance function. The pluged-in Bayes discriminant function is constructed by using ML estimators of unknown mean and anisotropy ratio parameters. We focus on the asymptotic approximation of expected error rate (AER) and our aim is to investigate the effects of two different spatial sampling designs (based on increasing and fixed domain asymptotics) on AER.

Keywords

• Bayes discriminant function
• actual risk
• expected error rate
• Gaussian random field
• increasing domain asymptotics
• infill asymptotics