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- W2502405257 abstract "This PhD thesis studies two fields of Statistics: Aggregation of estimatorsand shape constrained regression.Shape constrained regression studies the regression problem (find a function that approximates well a set of points) with an underlying shape constraint, that is, the function must have a specific shape. For instance, this function could be nondecreasing of convex: These two shape examples are the most studied. We study two estimators: an estimator based on aggregation methods and the Least Squares estimator with a convex shape constraint. Oracle inequalities are obtained for both estimators, and we construct confidence sets that are adaptive and honest.Aggregation of estimators studies the following problem. If several methods are proposed for the same task, how to construct a new method that mimics the best method among the proposed methods? We will study these problems in three settings: aggregation of density estimators, aggregation of affine estimators and aggregation on the regularization path of the Lasso." @default.
- W2502405257 created "2016-08-23" @default.
- W2502405257 creator A5009114084 @default.
- W2502405257 date "2016-06-28" @default.
- W2502405257 modified "2023-09-27" @default.
- W2502405257 title "Sharp oracle inequalities in aggregation and shape restricted regression" @default.
- W2502405257 hasPublicationYear "2016" @default.
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