Multivariate intensity estimation via hyperbolic wavelet selection

Nathalie Akakpo

Journal of Multivariate Analysis, 2017, vol. 161, issue C, 32-57

Abstract: We propose a new statistical procedure that can overcome the curse of dimensionality without structural assumptions on the function to estimate. It relies on a least-squares type penalized criterion and a new collection of models built from hyperbolic biorthogonal wavelet bases. We study its properties in a unifying intensity estimation framework, where an oracle-type inequality and adaptation to mixed smoothness are shown to hold. We also show how to implement the estimator with an algorithm whose complexity is manageable.

Keywords: Biorthogonal wavelets; Copula; Density; Hyperbolic wavelets; Lévy process; Mixed smoothness; Model selection; Poisson process (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:161:y:2017:i:c:p:32-57

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DOI: 10.1016/j.jmva.2017.07.005

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