A generic all-purpose transformation for multivariate modeling through copulas
Tóm tắt
Copulas have been used in various applications in biomedical sciences and finance. We suggest copulas as the generic all-purpose transformations which can enable one to apply various standard multivariate procedures more efficiently and with better statistical properties and results. More specifically, we consider the problem of transformation of any continuous data to multivariate normality using copulas as a device for defining the transformation. Such a transformation effectively enables us to model a variety of problems involving non-normal data using the classical multivariate statistical techniques. We evaluate and illustrate various applications including those in regression, multicollinearity, principal component analysis, factor analysis, partial least square modeling and structural equation modeling where analyses using the appropriate copula transformations result in substantial improvement in implementation, interpretation, prediction as well as in the corresponding models. A great many datasets available in the literature are analyzed which amply demonstrate the power of such an approach.
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