Efficient estimation of linear functionals of a bivariate distribution with equal, but unknown marginals: the least-squares approach

Hanxiang Peng and Anton Schick

Journal of Multivariate Analysis, 2005, vol. 95, issue 2, 385-409

Abstract: In this paper, we characterize and construct efficient estimators of linear functionals of a bivariate distribution with equal marginals. An efficient estimator equals the empirical estimator minus a correction term and provides significant improvements over the empirical estimator. We construct an efficient estimator by estimating the correction term. For this we use the least-squares principle and an estimated orthonormal basis for the Hilbert space of square-integrable functions under the unknown equal marginal distribution. Simulations confirm the asymptotic behavior of this estimator in moderate sample sizes and the considerable theoretical gains over the empirical estimator.

Keywords: Least; dispersed; regular; estimator; Least-squares; estimators; Efficient; influence; function; Empirical; estimator; Local; asymptotic; normality (search for similar items in EconPapers)
Date: 2005
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Citations: View citations in EconPapers (5)

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