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Christophe GAILLAC (TSE Toulouse) – "Adaptive estimation in the linear random coefficients model when regressors have limited variation"
Time: 2:00 pm – 3:15 pm
Date: 27th of January 2020
Place: Room 3001.
Christophe GAILLAC (TSE Toulouse) – “Adaptive estimation in the linear random coefficients model when regressors have limited variation”
We consider adaptive estimation of the joint distribution of intercept and slopes in a linear random coefficients model, allowing the regressors to be bounded. Allowing for heterogeneous coefficients (e.g. tastes, effects) and making inference on their distribution in a nonparametric way is important in many areas of science. Its use has been limited by the fact that a usual assumption is that the regressors have support the whole space R^p which is almost never satisfied in practice. Using tools from harmonic analysis related to analytic continuation that we have recently extended in https://arxiv.org/abs/1905.11338. This paper allows for regressors which are bounded when the slopes do not have heavy tails. The analysis of this problem falls in the field of severely ill posed statistical inverse problem. We provide a detailed analysis including lower bounds and an adaptive estimator and study various smoothness assumptions.
Joint work with Eric Gautier. Working paper available at https://arxiv.org/abs/1905.06584
Cristina BUTUCEA, Alexandre TSYBAKOV, Julie JOSSE, Eric MOULINES, Mathieu ROSENBAUM