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A generic all-purpose transformation for multivariate modeling through copulas

  • Manoj Bahuguna
  • Ravindra KhattreeEmail author
Regular Paper
  • 28 Downloads

Abstract

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.

Keywords

Copula Gaussian copula Linear models Multivariate modeling Multivariate normality Transformations 

Notes

Acknowledgements

The authors wish to thank the associate editor and two referees for their critical comments leading to the improvement in this work.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsOakland UniversityRochesterUSA
  2. 2.Department of Mathematics and Statistics, and Center for Data Science and Big Data AnalyticsOakland UniversityRochesterUSA

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