Multivariate intensity estimation via hyperbolic wavelet selection

JOURNAL OF MULTIVARIATE ANALYSIS

卷:161

Article

Akakpo, Nathalie^1,2 

[1] UPMC, LPMA, UMR 7599, Paris, France

[2] Univ Montreal, CRM, UMI 3457, Montreal, PQ, Canada

关键词: Biorthogonal wavelets;    Copula;    Density;    Hyperbolic wavelets;    Levy process;    Mixed smoothness;    Model selection;    Poisson process;   

DOI  :  10.1016/j.jmva.2017.07.005

来源: Elsevier

【 摘 要 】

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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free