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Relative cost curves: An alternative to AUC and an extension to 3-class problems

Olga Montvida, Frank Klawonn (2014)

Kybernetika

Performance evaluation of classifiers is a crucial step for selecting the best classifier or the best set of parameters for a classifier. Receiver Operating Characteristic (ROC) curves and Area Under the ROC Curve (AUC) are widely used to analyse performance of a classifier. However, the approach does not take into account that misclassification for different classes might have more or less serious consequences. On the other hand, it is often difficult to specify exactly the consequences or costs...

Remark on properties of bases for additive logratio transformations of compositional data

Karel Hron (2008)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

The statistical analysis of compositional data, multivariate data when all its components are strictly positive real numbers that carry only relative information and having a simplex as the sample space, is in the state-of-the-art devoted to represent compositions in orthonormal bases with respect to the geometry on the simplex and thus provide an isometric transformation of the data to an usual linear space, where standard statistical methods can be used (e.g. [2], [4], [5], [9]). However, in some...

Remarks on Two Product-like Constructions for Copulas

Fabrizio Durante, Erich Peter Klement, José Quesada-Molina, Peter Sarkoci (2007)

Kybernetika

We investigate two constructions that, starting with two bivariate copulas, give rise to a new bivariate and trivariate copula, respectively. In particular, these constructions are generalizations of the * -product and the ☆ -product for copulas introduced by Darsow, Nguyen and Olsen in 1992. Some properties of these constructions are studied, especially their relationships with ordinal sums and shuffles of Min.

Ridge estimation of covariance matrix from data in two classes

Yi Zhou, Bin Zhang (2024)

Applications of Mathematics

This paper deals with the problem of estimating a covariance matrix from the data in two classes: (1) good data with the covariance matrix of interest and (2) contamination coming from a Gaussian distribution with a different covariance matrix. The ridge penalty is introduced to address the problem of high-dimensional challenges in estimating the covariance matrix from the two-class data model. A ridge estimator of the covariance matrix has a uniform expression and keeps positive-definite, whether...

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....

Robustness regions for measures of risk aggregation

Silvana M. Pesenti, Pietro Millossovich, Andreas Tsanakas (2016)

Dependence Modeling

One of risk measures’ key purposes is to consistently rank and distinguish between different risk profiles. From a practical perspective, a risk measure should also be robust, that is, insensitive to small perturbations in input assumptions. It is known in the literature [14, 39], that strong assumptions on the risk measure’s ability to distinguish between risks may lead to a lack of robustness. We address the trade-off between robustness and consistent risk ranking by specifying the regions in...

Rotation to physiological factors revised

Miroslav Kárný, Martin Šámal, Josef Böhm (1998)

Kybernetika

Reconstruction of underlying physiological structures from a sequence of images is a long-standing problem which has been solved by factor analysis with a success. This paper tries to return to roots of the problem, to exploit the available findings and to propose an improved paradigm.

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