# Statistical Methods Utilizing Copulas

Statistical Methods Utilizing Copulas
Chair: Zhenhua Lin (University of Toronto)
[PDF]

ELIF ACAR, University of Manitoba
Conditional Copula Models for Right-Censored Clustered Event Time Data  [PDF]

This work proposes a modelling strategy to infer the impact of a covariate on the dependence structure of right-censored clustered event time data. The joint survival function of the event times is modelled using a parametric conditional copula whose parameter depends on a cluster-level covariate. We use a local likelihood approach to estimate the form of the copula parameter and outline a generalized likelihood ratio-type test strategy to formally test its constancy. We apply the methods to data from the Diabetic Retinopathy Study to assess the impact of disease onset age on the loss of visual acuity.

TARIK BAHRAOUI, Université de Sherbrooke
A Family of Goodness-of-fit Tests for Copulas Based on Characteristic Functions  [PDF]

A general class of rank statistics based on the characteristic function is introduced for testing composite goodness-of-fit hypotheses about multivariate copula families. These statistics are defined as L2 weighted functional distances between a nonparametric estimator and a semi-parametric estimator of the characteristic function associated to a copula. It is shown that these statistics behave asymptotically as a degenerate V-statistic of order 4 and that the limit distribution is, up to a constant, a weighted sum of independent chi-square random variables. A parametric bootstrap is suggested. At the end, simulation study and illustrated on a multivariate dataset

MANOJ BAHUGUNA, Oakland University, Rochester, MI
Copula Transformation, Prediction and Exploration  [PDF]

Copulas have been used in various applications in biomedical sciences and finance. In this talk, we suggest copula as a generic all-purpose transformation which can enable one to apply various standard procedures more efficiently and with better statistical properties and results. We evaluate and illustrate various applications including those in regression, principal component analysis and factor analysis, where analysis using the copula transformation results in improvement in implementation, interpretation as well as prediction. Specifically, emphasis is in introducing the multivariate normality using this all purpose transformation.

CAREN HASLER, University of Toronto
Vine Copulas for Imputation of Monotone Non-Response  [PDF]

We investigate the use of vines to impute for monotone non-response. We use vine copulas and factorize the density of the observed variables into a cascade of bivariate copulas to flexibly model their joint distribution. The structure of the vine depends on the non-response pattern. We build on the work of Aas et al. (2009) and propose a method to estimate the parameters of the bivariate copulas entering into the model. Imputations are carried out by simulating the missing values using the constructed model. We discuss the generalization of our results to more global non-response patterns. Project supported by CANSSI.

DAVID LEE, University of British Columbia
Multivariate Extreme Value Copulas with Factor and Tree Dependence Structures  [PDF]

In multivariate modelling, factor and tree dependence structures are parsimonious assumptions often reasonable in practice, for example in finance where stock prices are driven by common latent factors, or in spatial applications where stations form a tree network. We propose copula extensions for extreme observations that incorporate such structures. These models allow intuitive interpretation of dependence relationships underlying the processes that generate the extremes; this is illustrated through a data example, which also suggests that our proposed models may perform better than a fully unconstrained one.

YASSIR RABHI, Université de Sherbrooke
Copula Function Under Biased Sampling and Informative Censoring  [PDF]

In observational studies, incidence cohort sampling is ideally adopted to study individuals, who have not experienced a disease, from disease onset to a failure event. Logistic or other constraints may however preclude the possibility of recruiting incident cases. A feasible alternative in such circumstances is to sample subjects who have already experienced the disease onset, through cross-sectional sampling. In this presentation, we discuss the estimation of the copula function for right-censored length-biased data. Copula function is known for its use in modeling the dependence structure between two variables. We introduce a nonparametric estimation method for the copula and its functionals.