Empirical processes based on pseudo-observations II:: The multivariate case

One often needs to estimate the distribution functions of a random vector epsilon = H(X), where the H is unknown and might depend on the law of X. When H is estimated by some H,, using a sample X-1,...,X-n, the H-n(X-i)'s are termed pseudo-observations. In a semiparametric context, one often wants to estimate parameters related to the law of the non-observable epsilon. The transformed data H-n(X-1),..., H-n(X-n) are then naturally used, introducing dependence. Classical techniques do not apply and hard work is needed to get the asymptotic behaviour of estimators and empirical processes. The aim of this paper is to give a unified treatment of inference procedures based on pseudo-observations in the multivariate setting. Examples of applications are given.