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Martin KROLL (ENSAE-ParisTech CREST) – “On minimax optimal and adaptive estimation of linear functionals in inverse Gaussian sequence space models”
November 6, 2017, 2:00 pm - 3:15 pm
The Statistical Seminar: Every Monday at 2:00 pm.
Time: 2:00 pm – 3:15 pm
Date: 6th of November 2017
Place: Room 3001.
Martin KROLL (ENSAE-ParisTech CREST) “On minimax optimal and adaptive estimation of linear functionals in inverse Gaussian sequence space models“
We consider an inverse problem in a Gaussian sequence space model where the multiplication operator is not known but only available via noisy observations. Our aim is not to reconstruct the solution itself but the value of a linear functional of the solution. In our setup the optimal rate depends on two different noise levels, the noise level concerning the observation of the transformed solution and the noise level concerning the noisy observation of the operator. We consider this problem from a minimax point of view and obtain upper and lower bounds under smoothness assumptions on the multiplication operator and the unknown solution. Finally, we sketch an approach to the adaptive estimation in the given model using a method combining both model selection and the Goldenshluger-Lepski method.
This is joint work in progress with Cristina Butucea (ENSAE) and Jan Johannes (Heidelberg).
Cristina BUTUCEA, Alexandre TSYBAKOV, Eric MOULINES, Mathieu ROSENBAUM