Adaptive estimation in circular functional linear models.

Abstract : We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an orthogonal series estimator of the slope function, by replacing the first m theoretical coefficients of its development in the trigonometric basis by adequate estimators. Wepropose a model selection procedure for m in a set of admissible values, by defining a contrast function minimized by our estimator and a theoretical penalty function; this first step assumes the degree of ill posedness to be known. Then we generalize the procedure to a random set of admissible m's and a random penalty function. The resulting estimator is completely data driven and reaches automatically what is known to be the optimal minimax rate of convergence, in term of a general weighted L2-risk. This means that we provide adaptive estimators of both the slope function and its derivatives.
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Mathematical Methods of Statistics, Allerton Press, Springer (link), 2010, 19 (1), pp.42-63. <10.3103/S1066530710010035>
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Dernière modification le : mardi 11 octobre 2016 - 13:27:57
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Fabienne Comte, Jan Johannes. Adaptive estimation in circular functional linear models.. Mathematical Methods of Statistics, Allerton Press, Springer (link), 2010, 19 (1), pp.42-63. <10.3103/S1066530710010035>. <hal-00410729>

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