منابع مشابه
Locally Adaptive Confidence Bands
We develop honest and locally adaptive confidence bands for probability densities. They provide substantially improved confidence statements in case of inhomogeneous smoothness, and are easily implemented and visualized. The article contributes conceptual work on locally adaptive inference as a straightforward modification of the global setting imposes severe obstacles for statistical purposes....
متن کاملAdaptive Confidence Bands
We show that there do not exist adaptive confidence bands for curve estimation except under very restrictive assumptions. We propose instead to construct adaptive bands that cover a surrogate function f which is close to, but simpler than, f . The surrogate captures the significant features in f . We establish lower bounds on the width for any confidence band for f and construct a procedure tha...
متن کاملAdaptive Confidence Bands for Nonparametric Regression Functions.
A new formulation for the construction of adaptive confidence bands in non-parametric function estimation problems is proposed. Confidence bands are constructed which have size that adapts to the smoothness of the function while guaranteeing that both the relative excess mass of the function lying outside the band and the measure of the set of points where the function lies outside the band are...
متن کاملAnti-concentration and honest, adaptive confidence bands
Modern construction of uniform confidence bands for nonparametric densities (and other functions) often relies on the the classical Smirnov-Bickel-Rosenblatt (SBR) condition; see, for example, Giné and Nickl (2010). This condition requires the existence of a limit distribution of an extreme value type for the supremum of a studentized empirical process (equivalently, for the supremum of a Gauss...
متن کاملSupplement to “Adaptive Confidence Bands for Nonparametric Regression Functions”
This supplement contains the proofs of Theorem 2, Propositions 2 and 3, Lemma 1 and Eq.(14). 7 Proof of Theorem 2 Rather than prove Theorem 2 directly it is convenient to first prove an analogue of the Theorem in the context of multivariate Normal random vectors. This is done in section 7.1. The proof of Theorem 2 is then given in section 7.2 7.1 Confidence Bound For Multivariate Normal Vectors...
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ژورنال
عنوان ژورنال: The Annals of Statistics
سال: 2019
ISSN: 0090-5364
DOI: 10.1214/18-aos1690