Universal pointwise selection rule in multivariate function estimation

By Alexander Goldenshluger, O. Lepski. 2008

88 citations recorded by the source corpus.

In this paper, we study the problem of pointwise estimation of a multivariate function. We develop a gen eral 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 selec tion procedure specialized for different collections of estimators leads to minimax and adaptive minimax estimators in various settings.

Subfields: Finance, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/800fec260ab6fcd101fd1b0f46bf113a5c553f0d

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Citations in the corpus

Sharp Oracle Inequalities for Aggregation of Affine Estimators (2011, background): “Interestingly, although several recent papers [3, 5, 34] discuss the paradigm of competing against the best linear procedure from a given family, none of them provide oracle inequalities with leading constant equal to one.”
A tutorial on kernel density estimation and recent advances (2017, methodology): “In addition to the above approaches, [35] proposes a method, known as the Lepski’s approach [36,37], that treats the bandwidth selection problem as a model selection problem and proposes a new criterion for selecting the smoothing bandwidth.”
Bandwidth selection in kernel density estimation: Oracle inequalities and adaptive minimax optimality (2010, background): “Deﬁne also For every h ∈ H let Then the selected bandwidth ˆ h and the corresponding kernel density estimator are deﬁned by ˆ h := arg inf The selection rule (6)–(8) is a reﬁnement of the one introduced recently in Goldenshluger and Lepski (2008, 2009) for the Gaussian white noise model.”