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2018 Asymptotic confidence bands in the Spektor-Lord-Willis problem via kernel estimation of intensity derivative
Bogdan Ćmiel, Zbigniew Szkutnik, Jakub Wojdyła
Electron. J. Statist. 12(1): 194-223 (2018). DOI: 10.1214/18-EJS1391

Abstract

The stereological problem of unfolding the distribution of spheres radii from linear sections, known as the Spektor-Lord-Willis problem, is formulated as a Poisson inverse problem and an $L^{2}$-rate-minimax solution is constructed over some restricted Sobolev classes. The solution is a specialized kernel-type estimator with boundary correction. For the first time for this problem, non-parametric, asymptotic confidence bands for the unfolded function are constructed. Automatic bandwidth selection procedures based on empirical risk minimization are proposed. It is shown that a version of the Goldenshluger-Lepski procedure of bandwidth selection ensures adaptivity of the estimators to the unknown smoothness. The performance of the procedures is demonstrated in a Monte Carlo experiment.

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Bogdan Ćmiel. Zbigniew Szkutnik. Jakub Wojdyła. "Asymptotic confidence bands in the Spektor-Lord-Willis problem via kernel estimation of intensity derivative." Electron. J. Statist. 12 (1) 194 - 223, 2018. https://doi.org/10.1214/18-EJS1391

Information

Received: 1 September 2016; Published: 2018
First available in Project Euclid: 8 February 2018

zbMATH: 1387.62061
MathSciNet: MR3760886
Digital Object Identifier: 10.1214/18-EJS1391

Subjects:
Primary: 45Q05, 62G05, 62G20

JOURNAL ARTICLE
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Vol.12 • No. 1 • 2018
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