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Estimation of linear functionals of bivariate distributions with parametric marginals

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  • Peng Hanxiang
  • Schick Anton

Abstract

In this paper we construct estimators for linear functionals of bivariate distributions with parametric marginals. Our construction generalizes the construction of efficient estimators given by Peng and Schick (2002) for the case of known marginals. More precisely, we show that in their construction the fixed and known orthonormal bases for the Hilbert spaces of square integrable functions with zero means can now be replaced by estimated orthonormal bases using a n1/2-consistent estimator of the parameter.

Suggested Citation

  • Peng Hanxiang & Schick Anton, 2004. "Estimation of linear functionals of bivariate distributions with parametric marginals," Statistics & Risk Modeling, De Gruyter, vol. 22(1/2004), pages 61-78, January.
    • Handle: RePEc:bpj:strimo:v:22:y:2004:i:1/2004:p:61-78:n:5
    DOI: 10.1524/stnd.22.1.61.32714
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    References listed on IDEAS

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    1. 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.
    2. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
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