Electronic Journal of Statistics

Adaptive confidence sets for kink estimation

Viktor Bengs and Hajo Holzmann

Full-text: Open access

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.

Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 1523-1579.

Dates
Received: October 2018
First available in Project Euclid: 16 April 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1555380050

Digital Object Identifier
doi:10.1214/19-EJS1555

Mathematical Reviews number (MathSciNet)
MR3939304

Zentralblatt MATH identifier
07056157

Keywords
Adaptive estimation change-point estimation limit theorem nonparametric statistics Lepski’s method Z-estimation

Rights
Creative Commons Attribution 4.0 International License.

Citation

Bengs, Viktor; Holzmann, Hajo. Adaptive confidence sets for kink estimation. Electron. J. Statist. 13 (2019), no. 1, 1523--1579. doi:10.1214/19-EJS1555. https://projecteuclid.org/euclid.ejs/1555380050


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