Functionals of order statistics and their multivariate concomitants with application to semiparametric estimation by nearest neighbours

This paper studies the limiting behavior of general functionals of order statistics and their multivariate concomitants for weakly dependent data. The asymptotic analysis is performed under a conditional moment-based notion of dependence for vector-valued time series. It is argued, through analysis of various examples, that the dependence conditions of this type can be effectively implied by other dependence formations recently proposed in time-series analysis, thus it may cover many existing linear and nonlinear processes. The utility of this result is then illustrated in deriving the asymptotic properties of a semiparametric estimator that uses the k-Nearest Neighbour estimator of the inverse of a multivariate unknown density. This estimator is then used to calculate consumer surpluses for electricity demand in Ontario for the period 1971 to 1994. A Monte Carlo experiment also assesses the effi- cacy of the derived limiting behavior in finite samples for both these general functionals and the proposed estimator.