Bernoulli

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  • Volume 12, Number 4 (2006), 633-661.

Penalized projection estimators of the Aalen multiplicative intensity

Patricia Reynaud-Bouret

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Abstract

We study the problem of nonparametric, completely data-driven estimation of the intensity of counting processes satisfying the Aalen multiplicative intensity model. To do so, we use model selection techniques and, specifically, penalized projection estimators for a random inner product. For histogram estimators, under some assumptions on the process, we obtain adaptive results for the minimax risk. In general, for more intricate (predictable) models, we only obtain oracle inequalities. The study is complemented by some simulations in the right-censoring model.

Article information

Source
Bernoulli, Volume 12, Number 4 (2006), 633-661.

Dates
First available in Project Euclid: 16 August 2006

Permanent link to this document
https://projecteuclid.org/euclid.bj/1155735930

Digital Object Identifier
doi:10.3150/bj/1155735930

Mathematical Reviews number (MathSciNet)
MR2248231

Zentralblatt MATH identifier
1125.62027

Keywords
adaptive estimation counting processes model selection multiplicative intensity model penalized projection estimators

Citation

Reynaud-Bouret, Patricia. Penalized projection estimators of the Aalen multiplicative intensity. Bernoulli 12 (2006), no. 4, 633--661. doi:10.3150/bj/1155735930. https://projecteuclid.org/euclid.bj/1155735930


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References

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