Asymptotic approximation for the expected risk in classification of different spatial regressions. (English) Zbl 0980.62087

Dučinskas, K.; Saltyte, J.

Theory Probab. Math. Stat. 61, 15-20 (2000) and Teor. Jmovirn. Mat. Stat. 61, 15-20 (2000).

Let \(\{Z(s);\;s\in D\subset R^{2}\}\) be an intrinsically stationary Gaussian random field with different mean and spatial covariance functions under populations \(\Omega_{1}\) and \(\Omega_{2}.\) This paper deals with the following model of \(Z(s)\) in population \(\Omega_{l}\): \[ Z(s)=x'(s)\beta_{l}+\varepsilon_{l}(s), \] where \(x'(s)\) is a \(q\times 1\) vector of nonrandom regressors, \(\beta_{l},\;l=1,2,\) are parameter vectors in \(R^{q},\) and \(\varepsilon_{l}(s)\) is a zero-mean intrinsically stationary Gaussian random field with spatial covariance defined by a parametric model. The attention is restricted to homoscedastic models. The problem of classifying observations from spatial regression models is considered. Asymptotic approximations for the expected risk of a plug-in classification rule are obtained. Maximum likelihood estimators (MLE) of means and bias adjusted MLEs of variance are used in plug-in versions of the Bayes classification rule. Comparisons of the obtained asymptotic approximations with Monte Carlo simulations are presented.

Reviewer: A.V.Swishchuk (Kyïv)

MSC:

62M40	Random fields; image analysis
62H30	Classification and discrimination; cluster analysis (statistical aspects)
62M30	Inference from spatial processes
62H12	Estimation in multivariate analysis

Keywords:

spatial regression model; stationary Gaussian residuals; spatial correlation functions; expected risk; Monte Carlo simulations