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Estimating a bivariate density when there are extra data on one or both components

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  • Peter Hall
  • Natalie Neumeyer

Abstract

The objective of this paper is to estimate a bivariate density nonparametrically from a dataset from the joint distribution and datasets from one or both marginal distributions. We develop a copula-based solution, which has potential benefits even when the marginal datasets are empty. For example, if the copula density is sufficiently smooth in the region where we wish to estimate it, the joint density can be estimated with a high degree of accuracy. Similar improvements in performance are available if the marginals are close to being independent. We use wavelet estimators to approximate the copula density, which in cases of statistical interest can be unbounded along boundaries. Our techniques are also useful for solving recently-considered related problems, for example where the marginal distributions are determined by parametric models. The methodology is also readily extended to more general multivariate settings. Copyright 2006, Oxford University Press.

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  • Peter Hall & Natalie Neumeyer, 2006. "Estimating a bivariate density when there are extra data on one or both components," Biometrika, Biometrika Trust, vol. 93(2), pages 439-450, June.
    • Handle: RePEc:oup:biomet:v:93:y:2006:i:2:p:439-450
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    File URL: http://hdl.handle.net/10.1093/biomet/93.2.439
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    Cited by:

    1. Dimitrova, Dimitrina S. & Kaishev, Vladimir K. & Penev, Spiridon I., 2008. "GeD spline estimation of multivariate Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3570-3582, March.
    2. Qu, Leming & Yin, Wotao, 2012. "Copula density estimation by total variation penalized likelihood with linear equality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 384-398.

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