Limit Behaviour of Sequential Empirical Measure Processes

enables to reconstruct the whole sequence X1, ...,Xn (rather than the sample up to a permutation) makes of Pn a very flexible tool to represent complex and highly non-symmetric statistics. One can, for instance think of two-sample sequential rank statistics, V -statistics or fractional ARIMA processes as treated in Barbe and Broniatowski [1997] , [1998a] and [1998b]. In these references, sequential empirical measure representations allowed to obtain functional large deviation principles for classes of complex statistics as the ones evoked. Weak convergence in the case in which Q = { 1[0,t] · f : 0 < t ≤ 1, f ∈ F }