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Cox process functional learning

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  • Gérard Biau
  • Benoît Cadre
  • Quentin Paris

Abstract

This article addresses the problem of functional supervised classification of Cox process trajectories, whose random intensity is driven by some exogenous random covariable. The classification task is achieved through a regularized convex empirical risk minimization procedure, and a non asymptotic oracle inequality is derived. We show that the algorithm provides a Bayes-risk consistent classifier. Furthermore, it is proved that the classifier converges at a rate which adapts to the unknown regularity of the intensity process. Our results are obtained by taking advantage of martingale and stochastic calculus arguments, which are natural in this context and fully exploit the functional nature of the problem. Copyright Springer Science+Business Media Dordrecht 2015

Suggested Citation

  • Gérard Biau & Benoît Cadre & Quentin Paris, 2015. "Cox process functional learning," Statistical Inference for Stochastic Processes, Springer, vol. 18(3), pages 257-277, October.
    • Handle: RePEc:spr:sistpr:v:18:y:2015:i:3:p:257-277
    DOI: 10.1007/s11203-015-9115-z
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    References listed on IDEAS

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    1. Bartlett, Peter L. & Jordan, Michael I. & McAuliffe, Jon D., 2006. "Convexity, Classification, and Risk Bounds," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 138-156, March.
    2. Amparo Baíllo & Antonio Cuevas & Juan Antonio Cuesta‐Albertos, 2011. "Supervised Classification for a Family of Gaussian Functional Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(3), pages 480-498, September.
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