Statistical Classification of the Observation of Nuggetless Spatial Gaussian Process with Unknown Sill Parameter

The problem of classification of spatial Gaussian process observation into one of two populations specified by different regression mean models and common stationary covariance with unknown sill parameter is considered. Unknown parameters are estimated from training sample and these estimators are plugged in the Bayes discriminant function. The asymptotic expansion of the expected error rate associated with Bayes plug-in discriminant function is derived. Numerical analysis of the accuracy of approximation based on derived asymptotic expansion in the small training sample case is carried out. Comparison of two spatial sampling designs based on values of this approximation is done

Comparison of Nonlinear Spatial Correlation Models by the Influence of the Data Augmentation to the Classification Risk

The Bayesian classification rule used for the classification of the observations of the (second-order) stationary Gaussian random fields with different means and common factorised covariance matrices is investigated. The influence of the observed data augmentation to the Bayesian risk is examined for three different nonlinear widely applicable spatial correlation models. The explicit expression of the Bayesian risk for the classification of augmented data is derived. Numerical comparison of these models by the variability of Bayesian risk in case of the first-order neighbourhood scheme is performed

Quadratic Discriminant Analysis of Spatially Correlated Data

The problem of classification of the realisation of the stationary univariate Gaussian random field into one of two populations with different means and different factorised covariance matrices is considered. In such a case optimal classification rule in the sense of minimum probability of misclassification is associated with non-linear (quadratic) discriminant function. Unknown means and the covariance matrices of the feature vector components are estimated from spatially correlated training samples using the maximum likelihood approach and assuming spatial correlations to be known. Explicit formula of Bayes error rate and the first-order asymptotic expansion of the expected error rate associated with quadratic plug-in discriminant function are presented. A set of numerical calculations for the spherical spatial correlation function is performed and two different spatial sampling designs are compared

Statistical classification based on observations of random Gaussian fields

The problem of classification of objects located in domain D ⊂ R2 based on observations of random Gaussian fields with a factorized covariance function is considered. The first‐order asymptotic expansion for the expected error regret is presented. Obtained numerical results allow us to compare suggested expansion for some widely applicable models of spatial covariance function. Statistinis klasifikavimas remiantis atsitiktinių Gauso laikų stebėjimais Santrauka Nagrinejamas uždavinys apie objektu iš srites D C R 2 klasifikavima, remiantis atsitiktiniu Gauso lauku stebejimais. Pateikti asimptotiniai laukiamos paklaidos iverčiai. Atlikus skaitinio modeliavimo eksperimenta naujasis skleidinys lyginamas su kitais žinomais skleidimais. First Published Online: 14 Oct 201

Comparison of two estimators of mean function in LDA of spatially correlated Gaussian data

The problem of linear discriminant analysis of an observation of Gaussian random field into one of two populations is considered. In this paper we analyze the performance of the plug‐in linear discriminant function, when unknown means are estimated from the training samples. The generalized least squares and the ordinary least squares estimators are used. Obtained asymptotic expansions for the expected error rate are compared numerically in the case of spherical models for population covariances. Dviejų vidurkio įvertinių palyginimas tiesinėje erdvėje koreliuotų Gauso stebėjimų diskriminantinėje analizėje Santrauka Straipsnyje sprendžiamas atsitiktinio Gauso lauko stebejimu tiesines diskriminantines analizes uždavinys dvieju klasiu atveju. Gauti pirmos eile asimptotiniai tiketinos klasifikavimo klaidos skleidiniai atvejui, kai i Bajeso klasifikavimo taisykle istatome maksimalaus tiketinumo bei empirini vidurkiu iverčius. Atliktas skaitinis asimptotiniu klasifikavimo klaidu palyginimas tam tikrai kaimynystes schemai bei sferinei koreliaciju funkcijai.  First Published Online: 14 Oct 201