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Statistical inference for compound regression

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This talk considers a general nonparametric regression model called the compound model. It contains as two special cases sparse additive regression and nonparametric regression with many covariates but possibly a small number of relevant covariates. A compound model is characterized by three main parameters: the “microscopic” sparsity parameter indicating the number of relevant covariates, the structure parameter, i.e., a binary sequence describing the “macroscopic” structure of the compound function and the usual smoothness parameter corresponding to the complexity of the members of the compound. We find non-asymptotic minimax rate of convergence of estimators in such a model as a function of these three parameters. We also show that this rate can be attained in an adaptive way. This is a joint work with Arnak Dalalyan and Yuri Ingster.

This talk is part of the Statistics series.

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