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On efficient estimation of linear functionals of a bivariate distribution with known marginals

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  • Peng, Hanxiang
  • Schick, Anton

Abstract

In this paper we construct efficient estimators for linear functionals of a bivariate distribution with known marginals. Previously, Bickel et al. (Ann. Statist. 19 (1991) 1316) constructed such estimators using the modified minimum chi-square principle. Our estimators utilize the least-squares principle and orthonormal bases for the Hilbert spaces of square integrable functions under the known marginal distributions and are easy to compute. Simulations indicate that in the moderate sample sizes considered our estimator compares favorably with the one proposed by Bickel et al.

Suggested Citation

  • Peng, Hanxiang & Schick, Anton, 2002. "On efficient estimation of linear functionals of a bivariate distribution with known marginals," Statistics & Probability Letters, Elsevier, vol. 59(1), pages 83-91, August.
    • Handle: RePEc:eee:stapro:v:59:y:2002:i:1:p:83-91
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    Citations

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    Cited by:

    1. Segers, J.J.J. & van den Akker, R. & Werker, B.J.M., 2008. "Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known," Discussion Paper 2008-40, Tilburg University, Center for Economic Research.
    2. Segers, J.J.J. & van den Akker, R. & Werker, B.J.M., 2008. "Improving Upon the Marginal Empirical Distribution Functions when the Copula is Known," Other publications TiSEM 950a8cda-8f8c-43a9-a5c2-8, Tilburg University, School of Economics and Management.
    3. Peng, Hanxiang & Schick, Anton, 2005. "Efficient estimation of linear functionals of a bivariate distribution with equal, but unknown marginals: the least-squares approach," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 385-409, August.
    4. Penev, Spiridon & Peng, Hanxiang & Schick, Anton & Wefelmeyer, Wolfgang, 2004. "Efficient estimators for functionals of Markov chains with parametric marginals," Statistics & Probability Letters, Elsevier, vol. 66(3), pages 335-345, February.
    5. Peng Hanxiang & Schick Anton, 2004. "Estimation of linear functionals of bivariate distributions with parametric marginals," Statistics & Risk Modeling, De Gruyter, vol. 22(1), pages 61-78, January.
    6. Peng Hanxiang & Schick Anton, 2004. "Efficient estimation of a linear functional of a bivariate distribution with equal, but unknown, marginals: The minimum chi-square approach," Statistics & Risk Modeling, De Gruyter, vol. 22(4), pages 301-318, April.

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