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

Chu, Ba and Huynh, Kim and Jacho-Chavez, David (2013): Functionals of order statistics and their multivariate concomitants with application to semiparametric estimation by nearest neighbours. Published in: Sankhya B , Vol. 75, No. 2 (2013): pp. 238-292.

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Abstract

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.

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