Publication: Non-parametric methods for circular-circular and circular-linear
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2011-04
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Abstract
We present a non-parametric approach for the estimation of the bivariate distribution of two
circular variables and the modelling of the joint distribution of a circular and a linear variable.
We combine nonparametric estimates of the marginal densities of the circular and linear
components with the use of class of nonparametric copulas, known as empirical Bernstein
copulas, to model the dependence structure. We derive the necessary conditions to obtain
continuous distributions defined on the cylinder for the circular-linear model and on the torus for
the circular-circular model. We illustrate these two approaches with two sets of real
environmental data
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Bernstein polynomials, Circular distributions, Circular-Circular data, Circular-linear data, Copulas, Non-parametric estimation