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Concept of Data Depth and Its Applications

Ondřej Vencálek (2011)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Data depth is an important concept of nonparametric approach to multivariate data analysis. The main aim of the paper is to review possible applications of the data depth, including outlier detection, robust and affine-equivariant estimates of location, rank tests for multivariate scale difference, control charts for multivariate processes, and depth-based classifiers solving discrimination problem.

Convergence model of interest rates of CKLS type

Zuzana Zíková, Beáta Stehlíková (2012)

Kybernetika

This paper deals with convergence model of interest rates, which explains the evolution of interest rate in connection with the adoption of Euro currency. Its dynamics is described by two stochastic differential equations – the domestic and the European short rate. Bond prices are then solutions to partial differential equations. For the special case with constant volatilities closed form solutions for bond prices are known. Substituting its constant volatilities by instantaneous volatilities we...

Copula-based grouped risk aggregation under mixed operation

Quan Zhou, Zhenlong Chen, Ruixing Ming (2016)

Applications of Mathematics

This paper deals with the problem of risk measurement under mixed operation. For this purpose, we divide the basic risks into several groups based on the actual situation. First, we calculate the bounds for the subsum of every group of basic risks, then we obtain the bounds for the total sum of all the basic risks. For the dependency relationships between the basic risks in every group and all of the subsums, we give different copulas to describe them. The bounds for the aggregated risk under mixed...

Correspondence analysis and two-way clustering.

Antonio Ciampi, Ana González Marcos, Manuel Castejón Limas (2005)

SORT

Correspondence analysis followed by clustering of both rows and columns of a data matrix is proposed as an approach to two-way clustering. The novelty of this contribution consists of: i) proposing a simple method for the selecting of the number of axes; ii) visualizing the data matrix as is done in micro-array analysis; iii) enhancing this representation by emphasizing those variables and those individuals which are 'well represented' in the subspace of the chosen axes. The approach is applied...

Covariance Structure of Principal Components for Three-Part Compositional Data

Klára Hrůzová, Karel Hron, Miroslav Rypka, Eva Fišerová (2013)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

Statistical analysis of compositional data, multivariate observations carrying only relative information (proportions, percentages), should be performed only in orthonormal coordinates with respect to the Aitchison geometry on the simplex. In case of three-part compositions it is possible to decompose the covariance structure of the well-known principal components using variances of log-ratios of the original parts. They seem to be helpful for the interpretation of these special orthonormal coordinates....

Cumulative processes related to event histories.

Cook, Richard, J. 1, Jerald F. Lawless, Ker-Ai Lee (2003)

SORT

Costs or benefits which accumulate for individuals over time are of interest in many life history processes. Familiar examples include costs of health care for persons with chronic medical conditions, the payments to insured persons during periods of disability, and quality of life which is sometimes used in the evaluation of treatments in terminally ill patients. For convenience, here we use the term costs to refer to cost or other cumulative measures. Two important scenarios are (i) where costs...

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