Minimax wavelet estimation for multisample heteroscedastic nonparametric regression

ABSTRACT

The problem of estimating the baseline signal from multisample noisy curves is investigated. We consider the functional mixed-effects model, and we suppose that the functional fixed effect belongs to the Besov class. This framework allows us to model curves that can exhibit strong irregularities, such as peaks or jumps for instance. The lower bound for the minimax risk is provided, as well as the upper bound of the minimax rate, that is derived by constructing a wavelet estimator for the functional fixed effect. Our work constitutes the first theoretical functional results in multisample nonparametric regression. Our approach is illustrated on realistic simulated datasets as well as on experimental data.

KEYWORDS:

• Functional mixed-effects models
• minimax risk
• Besov class
• wavelet estimator

Acknowledgments

We are grateful to Anatoli Juditsky for constructive and fruitful discussions. The authors would like to thank the reviewer team's constructive comments, which improve significantly the quality of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 http://home.ccr.cancer.gov/ncifdaproteomics/ppatterns.asp