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See detailA novel definition of the multivariate coefficient of variation
Albert, Adelin ULg; Zhang, Lixin ULg

in Biometrical Journal = Biometrische Zeitschrift (2010), 52(5), 667-675

The coefficient of variation CV (%) is widely used to measure the relative variation of a random variable to its mean or to assess and compare the performance of analytical techniques/equipments. A review ... [more ▼]

The coefficient of variation CV (%) is widely used to measure the relative variation of a random variable to its mean or to assess and compare the performance of analytical techniques/equipments. A review is made of the existing multivariate extensions of the univariate CV where, instead of a random variable, a random vector is considered, and a novel definition is proposed. The multivariate CV obtained only requires the calculation of the mean vector, the covariance matrix and simple quadratic forms. No matrix inversion is needed which makes the new approach equally attractive inhigh dimensional as in very small sample size problems. As an illustration, the method is applied to electrophoresis data from external quality assessment in laboratory medicine, to phenotypic characteristics of pocket gophers and to a microarray data set. [less ▲]

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See detailComparison between principal component analysis and independent component analysis in EEG modelling
Bugli, Céline; Lambert, Philippe ULg

in Biometrical Journal = Biometrische Zeitschrift (2007), 49

Principal Component Analysis (PCA) is a classical technique in statistical data analysis, feature extraction and data reduction, aiming at explaining observed signals as a linear combination of orthogonal ... [more ▼]

Principal Component Analysis (PCA) is a classical technique in statistical data analysis, feature extraction and data reduction, aiming at explaining observed signals as a linear combination of orthogonal principal components. Independent Component Analysis (ICA) is a technique of array processing and data analysis, aiming at recovering unobserved signals or ‘sources’ from observed mixtures, exploiting only the assumption of mutual independence between the signals. The separation of the sources by ICA has great potential in applications such as the separation of sound signals (like voices mixed in simultaneous multiple records, for example), in telecommunication or in the treatment of medical signals. However, ICA is not yet often used by statisticians. In this paper, we shall present ICA in a statistical framework and compare this method with PCA for electroencephalograms (EEG) analysis.We shall see that ICA provides a more useful data representation than PCA, for instance, for the representation of a particular characteristic of the EEG named event-related potential (ERP). [less ▲]

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See detailIntroducing the multivariate dale model in population-based genetic association studies
Van Steen, Kristel ULg; Tahri, N.; Molenberghs, G.

in Biometrical Journal = Biometrische Zeitschrift (2004), 46(2), 187-202

Until recently, the most common parametric approaches to study the combined effects of several genetic polymorphisms located within a gene or in a small genomic region are, at the genotype level, logistic ... [more ▼]

Until recently, the most common parametric approaches to study the combined effects of several genetic polymorphisms located within a gene or in a small genomic region are, at the genotype level, logistic regressions and at the haplotype level, haplotype analyses. An alternative modeling approach, based on the case/control principle, is to regard exposures (e.g., genetic data such as derived from Single Nucleotide Polymorphisms - SNPs) as random and disease status as fixed and to use a marginal multivariate model that accounts for inter-relationships between exposures. One such model is the multivariate Dale model. This model is based on multiple logistic regressions. That is why the model, applied in a case/control setting, leads to straightforward interpretations that are similar to those drawn in a classical logistic modeling framework. [less ▲]

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