ADAPTIVE ESTIMATION OF A QUADRATIC FUNCTIONAL BY MODEL SELECTION We want to present an adaptive estimation method based on model selection To better understand its interest and the way it works, it is useful to recall first the minimax approach for which one can use an estimator defined from a single finite-dimensional linear model
Adaptive estimation of a quadratic functional by model selection We prove a general nonasymptotic risk bound which allows us to show that such penalized estimators are adaptive on a variety of collections of sets for the parameter $s$, depending on the family
Adaptive estimation of a quadratic functional by model selection In particular, in the context of the Gaussian sequence model, a convenient choice of the family of models allows denning estimators which are adaptive over collections of hyperrectangles, ellipsoids, lp-bodies or Besov bodies
Adaptive estimation of a quadratic functional by model selection Our approach consists in considering some at most countable families of finite-dimensional linear subspaces of H H (the models) and then using model selection via some conveniently penalized least squares criterion to build new estimators of ∥s∥2 ‖ s ‖ 2
Adaptive Estimation of a Quadratic Functional by Model Selection - JSTOR Our approach consists in considering some at most countable families of finite-dimensional linear subspaces of H (the models) and then using model selection via some con-veniently penalized least squares criterion to build new estimators of IIs I2