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2019 Adaptive confidence sets for kink estimation
Viktor Bengs, Hajo Holzmann
Electron. J. Statist. 13(1): 1523-1579 (2019). DOI: 10.1214/19-EJS1555

Abstract

We consider estimation of the location and the height of the jump in the $\gamma $-th derivative - a kink of order $\gamma $ - of a regression curve, which is assumed to be Hölder smooth of order $s\geq \gamma +1$ away from the kink. Optimal convergence rates as well as the joint asymptotic normal distribution of estimators based on the zero-crossing-time technique are established. Further, we construct joint as well as marginal asymptotic confidence sets for these parameters which are honest and adaptive with respect to the smoothness parameter $s$ over subsets of the Hölder classes. The finite-sample performance is investigated in a simulation study, and a real data illustration is given to a series of annual global surface temperatures.

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Viktor Bengs. Hajo Holzmann. "Adaptive confidence sets for kink estimation." Electron. J. Statist. 13 (1) 1523 - 1579, 2019. https://doi.org/10.1214/19-EJS1555

Information

Received: 1 October 2018; Published: 2019
First available in Project Euclid: 16 April 2019

zbMATH: 07056157
MathSciNet: MR3939304
Digital Object Identifier: 10.1214/19-EJS1555

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