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Nonparametric Estimation of Multivariate Distributions with Given Marginals

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  • Sancetta, A.

Abstract

Nonparametric estimation of the copula function using Bernstein polynomials is studied. Convergence in the uniform topology is established. From the nonparametric Bernstein copula, the nonparametric Bernstein copula density is derived. It is shown that the nonparametric Bernstein copula density is closely related to the histogram estimator, but has the smoothing properties of kernel estimators. The optimal order of polynomial under the L2 norm is shown to be closely related to the inverse of the optimal smoothing factor for common nonparametric estimator. In order of magnitude, this estimator has variance equal to the square root of other common nonparametric estimators, e.g. kernel smoothers, but it is biased as a histogram estimator.

Suggested Citation

  • Sancetta, A., 2003. "Nonparametric Estimation of Multivariate Distributions with Given Marginals," Cambridge Working Papers in Economics 0320, Faculty of Economics, University of Cambridge.
    • Handle: RePEc:cam:camdae:0320
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    Cited by:

    1. Hall, Peter & Neumeyer, Natalie, 2005. "Estimating a bivariate density when there are extra data on one or both components," Technical Reports 2005,28, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Salmon, Mark & Schleicher, Christoph & Hurd, Matthew, 2005. "Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index," CEPR Discussion Papers 5114, C.E.P.R. Discussion Papers.

    More about this item

    Keywords

    Bernstein Polynomial; Copula; Course of Dimensionality; Histogram; Nonparametric Estimator.;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation

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