186,546 research outputs found
FILZMOSER P.: An object oriented framework for robust multivariate analysis
No full textThis introduction to the R package rrcov is a (slightly) modified version of Todorov and Filzmoser (2009), published in the Journal of Statistical Software. Taking advantage of the S4 class system of the programming environment R, which facil-itates the creation and maintenance of reusable and modular components, an object ori-ented framework for robust multivariate analysis was developed. The framework resides in the packages robustbase and rrcov and includes an almost complete set of algorithms for computing robust multivariate location and scatter, various robust methods for princi-pal component analysis as well as robust linear and quadratic discriminant analysis. The design of these methods follows common patterns which we call statistical design patterns in analogy to the design patterns widely used in software engineering. The application of the framework to data analysis as well as possible extensions by the development of new methods is demonstrated on examples which themselves are part of the package rrcov
An Object-Oriented Framework for Statistical Simulation: The R Package simFrame
No full textSimulation studies are widely used by statisticians to gain insight into the quality of developed methods. Usually some guidelines regarding, e.g., simulation designs, contamination, missing data models or evaluation criteria are necessary in order to draw meaningful conclusions. The R package simFrame is an object-oriented framework for statistical simulation, which allows researchers to make use of a wide range of simulation designs with a minimal effort of programming. Its object-oriented implementation provides clear interfaces for extensions by the user. Since statistical simulation is an embarrassingly parallel process, the framework supports parallel computing to increase computational performance. Furthermore, an appropriate plot method is selected automatically depending on the structure of the simulation results. In this paper, the implementation of simFrame is discussed in great detail and the functionality of the framework is demonstrated in examples for different simulation designs.
Identification of Multivariate Outliers: A Performance Study
No full textThree methods for the identification of multivariate outliers (Rousseeuw and Van Zomeren, 1990; Becker and Gather, 1999; Filzmoser et al., 2005) are compared. They are based on the Mahalanobis distance that will be made resistant against outliers and model deviations by robust estimation of location and covariance. The comparison is made by means of a simulation study. Not only the case of multivariate normally distributed data, but also heavy tailed and asymmetric distributions will be considered. The simulations are focused on low dimensional (p = 5) and high dimensional (p = 30) data.</jats:p
An Object-Oriented Framework for Robust Multivariate Analysis
No full textTaking advantage of the S4 class system of the programming environment R, which facilitates the creation and maintenance of reusable and modular components, an object-oriented framework for robust multivariate analysis was developed. The framework resides in the packages robustbase and rrcov and includes an almost complete set of algorithms for computing robust multivariate location and scatter, various robust methods for principal component analysis as well as robust linear and quadratic discriminant analysis. The design of these methods follows common patterns which we call statistical design patterns in analogy to the design patterns widely used in software engineering. The application of the framework to data analysis as well as possible extensions by the development of new methods is demonstrated on examples which themselves are part of the package rrcov.
A robust Parafac model for compositional data
No full textA robust Tucker3 model for three-way compositional data is presented. The algorithm to compute the Tucker3 parameters is based on ALS procedure implemented with robust alternative measures as Comedian and correlation median. The algorithm is able to capture the features of the complex structure, avoiding the information loss problem that occurs when two-way analysis techniques are adopted and the outliers effects. Some evidences are illustrated performing the model to macroeconomic compositional data
Simplicial principal component analysis for density functions in Bayes spaces
No full textProbability density functions are frequently used to characterize the distributional properties
of large-scale database systems. As functional compositions, densities primarily carry
relative information. As such, standard methods of functional data analysis (FDA) are not
appropriate for their statistical processing. The specific features of density functions are
accounted for in Bayes spaces, which result from the generalization to the infinite dimensional
setting of the Aitchison geometry for compositional data. The aim is to build up a
concise methodology for functional principal component analysis of densities. A simplicial
functional principal component analysis (SFPCA) is proposed, based on the geometry
of the Bayes space B2 of functional compositions. SFPCA is performed by exploiting the
centred log-ratio transform, an isometric isomorphism between B2 and L2 which enables
one to resort to standard FDA tools. The advantages of the proposed approach with respect
to existing techniques are demonstrated using simulated data and a real-world example of
population pyramids in Upper Austria
Logratio Approach to Distributional Modeling
No full textDistributional data, such as age distributions of populations, can be treated as continuous or discrete data, but the main interest is in the relative information, e.g., in terms of ratios (or logratios) between the different age classes. Here we present a unifying framework for the discrete and the continuous case based on the theory of Bayes spaces. While the discrete case is more widely treated in the literature, the continuous case allows to make a link to functional data analysis. Moreover, the methodological framework of Bayes spaces can also be used to develop methods for analyzing several distributional variables simultaneously. It turns out that the centered logratio transformation is a convenient tool for practical computations. Two real data examples illustrate the usefulness of this framework
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