Adaptive confidence sets in $$L^2$$

By Adam D. Bull, Richard Nickl. 2011

49 citations recorded by the source corpus.

The problem of constructing confidence sets that are adaptive in $$L^2$$-loss over a continuous scale of Sobolev classes of probability densities is considered. Adaptation holds, where possible, with respect to both the radius of the Sobolev ball and its smoothness degree, and over maximal parameter spaces for which adaptation is possible. Two key regimes of parameter constellations are identified: one where full adaptation is possible, and one where adaptation requires critical regions be removed. Techniques used to derive these results include a general nonparametric minimax test for infinite-dimensional null- and alternative hypotheses, and new lower bounds for $$L^2$$-adaptive confidence sets.

Subfields: Numerical Analysis, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/d54187d0a6f9559e8f52d9ab9780a2eaadd4820e

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Numerical Analysis

1. Sara A. van de Geer
2. Richard Nickl
3. Evarist Gin'e
4. Kengo Kato
5. Tengyuan Liang
6. Bharath K. Sriperumbudur

In Statistics and Probability

1. Sara A. van de Geer
2. Richard Nickl
3. Victor Chernozhukov
4. Kengo Kato
5. Bharath K. Sriperumbudur
6. Cun-Hui Zhang
7. I. Castillo
8. D. Chetverikov

Citations in the corpus

• Confidence sets in sparse regression (2012, methodology): “Theorem 2 reiterates the findings in Hoffmann and Nickl (2011) and Bull and Nickl (2013) that adaptive confidence sets exist over parameter spaces for which the structural property one wishes to adapt to–in the present case, sparsity— can be detected from the sample.”