ADAPTIVE PROJECTION ESTIMATION FOR A CLASS OF FUNCTIONAL PARAMETERS

Denis BOSQ

Univerité Pierre et Marie Curie
Paris, France


ABSTRACT

We consider estimation for a class of functional parameters which contains density and its derivatives, spectral density, covariance operators,....We show that adaptive projection estimators of these parameters reach a superoptimal rate on a dense set and optimal rates up to a logarithm elsewhere. The framework is discrete time processes with some extensions to continuous time processes.



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