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Functionals of order statistics and their multivariate concomitants with application to semiparametric estimation by nearest neighbours. (English) Zbl 1282.62128
Summary: 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, and 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 the consumer surplus for electricity demand in Ontario for the period 1971 to 1994. A Monte Carlo experiment also assesses the efficacy of the derived limiting behavior in finite samples for both these general functionals and the proposed estimator.

MSC:
 62G30 Order statistics; empirical distribution functions 62G20 Asymptotic properties of nonparametric inference 62H12 Estimation in multivariate analysis 62G05 Nonparametric estimation 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62P20 Applications of statistics to economics 65C05 Monte Carlo methods
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References:
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