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Practical estimation of multivariate densities using wavelet methods

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  • K. Tribouley

Abstract

This paper describes a practical method for estimating multivariate densities using wavelets. As in kernel methods, wavelet methods depend on two types of parameters. On the one hand we have a functional parameter: the wavelet Ø (comparable to the kernel K) and on the other hand we have a smoothing parameter: the resolution index (comparable to the bandwidth h). Classically, we determine the resolution index with a cross‐validation method. The advantage of wavelet methods compared to kernel methods is that we have a technique for choosing the wavelet Ø among a fixed family. Moreover, the wavelets method simplifies significantly both the theoretical and the practical computations.

Suggested Citation

  • K. Tribouley, 1995. "Practical estimation of multivariate densities using wavelet methods," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 49(1), pages 41-62, March.
    • Handle: RePEc:bla:stanee:v:49:y:1995:i:1:p:41-62
    DOI: 10.1111/j.1467-9574.1995.tb01454.x
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    Cited by:

    1. Autin, F. & Le Pennec, E. & Tribouley, K., 2010. "Thresholding methods to estimate copula density," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 200-222, January.
    2. Antonio Cosma & Olivier Scaillet & Rainer von Sachs, 2005. "Multiariate Wavelet-based sahpe preserving estimation for dependant observation," FAME Research Paper Series rp144, International Center for Financial Asset Management and Engineering.
    3. B. L. S. Prakasa Rao, 2010. "Wavelet linear estimation for derivatives of a density from observations of mixtures with varying mixing proportions," Indian Journal of Pure and Applied Mathematics, Springer, vol. 41(1), pages 275-291, February.

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