main advantage allowed to model separately the marginal distributions and the dependencies linking them together to produce the multivariate model subject of study
main advantage • allowed to model separately the marginal distributions and the dependencies linking them together to produce the multivariate model subject of study
Estimate p(x)from given samples Step 1: Construct estimates of the marginal pdfs p( T1),……,P(cd → cdfs P(x1),,P(xd) Step 2: Combine them d P(x)=p(a:)c(P(),P(rd)
Estimate p(x) from given samples Step 1: Construct estimates of the marginal pdfs → cdfs Step 2: Combine them
Estimate marginal pdfs and cdfs Parametric(copula ) manners Examples: Gaussian Gumbel. Frank Clayton or Student copulas, etc Weaknesses Real-world data often exhibit complex dependencies which cannot be correctly described
Estimate marginal pdfs and cdfs • Parametric (copula) manners Examples: Gaussian, Gumbel, Frank, Clayton or Student copulas, etc. Weaknesses: Real-world data often exhibit complex dependencies which cannot be correctly described!
stration of weaknesses Figure 2: Left, sample from the copula linking variables 4 and 1 1 in the WIRELESS dataset. Middle density estimate generated by a Gaussian copula model when fitted to the data. This technique is unable to capture the complex patterns present in the data. Right, copula density estimate generated by the non-parametric method described in section 2.1
Illustration of Weaknesses
Estimate marginal pdfs and cdfs Non-parametric manners Using unidimensional KDES llustration of estimation for Bivariate copulas
• Non-parametric manners Using unidimensional KDEs. • Illustration of estimation for Bivariate Copulas Estimate marginal pdfs and cdfs