  Copulas are mathematical objects that fully capture the dependence structure
among random variables and hence, offer a great flexibility in building
multivariate stochastic models. In statistics, a copula is used as a general
way of formulating a multivariate distribution in such a way that various
general types of dependence can be represented. In case of bivariate sample,
the notion of estimating copula is closely related to that of testing
independence in a bivariate sample, as when the components of the bivariate
sample are independent the copula becomes simply product of two uniform
distributions. So apart from non-parametric estimation of copulas we also
considered it relevant to introduce some non-parametric tests to better
understand the very essence of copula in the explanation of association between
the components. In fact we will develop a general multivariate statistics that
gives rise to a much larger class of non-parametric rank based statistics. This
class of statistics can be used in estimation and testing for the association
present in the bivariate sample. We choose some representative statistics from
that class and compared their power in testing independence using simulation as
an attempt to choose the best candidate in that class.
