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Multiplicative Algorithms for Density Combination and Deconvolution

In: Recent Advances in Econometrics and Statistics

Author

Listed:
  • Christine De Mol

    (Université libre de Bruxelles, Department of Mathematics and ECARES)

Abstract

In a previous paper by Conflitti et al. (Int J Forecasting 31:1096–1103, 2015), we devised a simple multiplicative iterative algorithm to compute the weights of an optimal combination of density forecasts. However, the question of convergence of this algorithm was not addressed. In the present work, we provide a detailed convergence proof, both for the cost function and for the sequence of iterates. We then show that a similar algorithm can be used for a classic problem in statistics, namely, the estimation of a mixture of known probability densities. The algorithm can be generalized to treat the case where the data are affected by a known noise, i.e., a density deconvolution problem. Finally, we address the situation of an unknown noise, assuming that it is itself a mixture of known densities, and we propose an adapted alternating blind deconvolution algorithm, the convergence properties of which are also analyzed.

Suggested Citation

  • Christine De Mol, 2024. "Multiplicative Algorithms for Density Combination and Deconvolution," Springer Books, in: Matteo Barigozzi & Siegfried Hörmann & Davy Paindaveine (ed.), Recent Advances in Econometrics and Statistics, pages 493-510, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-61853-6_25
    DOI: 10.1007/978-3-031-61853-6_25
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