About the estimation of multivariate functions and some related testing problems – Florent Autin
Florent Autin
I2M, Aix-Marseille Université
/user/florent.autin/
Date(s) : 24/04/2015 iCal
14h00 - 15h00
In this talk we are interested in both nonparametric multivariate function estimation and testing problems. In the first part of the talk, we provide wavelet-based methods to estimate functions with anisotropic smoothness and we study their good asymptotic properties thanks to the minimax and the maxiset approaches. In particular, we highlight the benefits from using hyperbolic wavelet bases and we discuss the curse of dimensionality. In the second part, we focus on hypothesis testing problems to detect the structure of multivariate functions. The testing procedures we propose are proved to be asymptotically optimal and to perform well in practice as it is shown by many numerical experiments.
References
Autin, F., Claeskens, G., Freyermuth, J.-M. (2014). Hyperbolic wavelet thresholding rules: the curse of dimensionality through the maxiset approach. Applied an Computational Harmonic Analysis, vol. 36, 239-255.
Autin, F., Claeskens, G., Freyermuth, J.-M. (2015). Asymptotic performance of projection estimators in standard and hyperbolic wavelet bases. Submitted to Bernoulli.
Autin, F., Claeskens, G., Freyermuth, J.-M., Pouet,C. (2015). Minimax optimal testing for structure of multivariate data. In redaction.
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