Universal pointwise selection rule in multivariate function estimation

Details Universal pointwise selection rule in multivariate function estimation Universal pointwise selection rule in multivariate function estimation

2008-11-17

arxiv.org/abs/0811.2649v1

Bernoulli 2008, Vol. 14, No. 4, 1150-1190

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/08-BEJ144 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/08-BEJ144

In this paper, we study the problem of pointwise estimation of a multivariate function. We develop a general pointwise estimation procedure that is based on selection of estimators from a large parameterized collection. An upper bound on the pointwise risk is established and it is shown that the proposed selection procedure specialized for different collections of estimators leads to minimax and adaptive minimax estimators in various settings.

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