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Robust estimation in the multivariate normal model

Agnieszka Kulawik;  Stefan Zontek — 2016

Discussiones Mathematicae Probability and Statistics

Robust estimation presented in the following paper is based on Fisher consistent and Fréchet differentiable statistical functionals. The method has been used in the multivariate normal model with variance components [5]. To transfer the method to estimate vector of expectations and positive definite covariance matrix of the multivariate normal model it is required to express the covariance matrix as a linear combination of basic elements of the vector space of real, square and symmetric matrices....

Robust estimation and its application to a classification problem

Henryk Gacki;  Agnieszka Kulawik — 2019

Mathematica Applicanda

In the article, a classification problem with two distributed classes is considered. The problem is solving using empirical discriminant functions for Gaussian classifier and estimators for unknown parameters of multivariate normal distribution. The three etimators, maximum likelihood estimator, Kulawik-Zontek estimator and minimum covariance determinant estimator, are compared in two different empirical examples (small size sample and large size sample).

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