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Descripción

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.

Pertenece a

Project Euclid (Hosted at Cornell University Library)  

Autor(es)

Ćmiel, Bogdan -  Szkutnik, Zbigniew -  Wojdyła, Jakub - 

Id.: 70979750

Idioma: inglés  - 

Versión: 1.0

Estado: Final

Tipo:  application/pdf - 

Palabras claveSpektor -  Lord -  Willis problem - 

Tipo de recurso: Text  - 

Tipo de Interactividad: Expositivo

Nivel de Interactividad: muy bajo

Audiencia: Estudiante  -  Profesor  -  Autor  - 

Estructura: Atomic

Coste: no

Copyright: sí

: Copyright 2018 The Institute of Mathematical Statistics and the Bernoulli Society

Formatos:  application/pdf - 

Requerimientos técnicos:  Browser: Any - 

Relación: [References] 1935-7524

Fecha de contribución: 17-feb-2018

Contacto:

Localización:
* Electron. J. Statist. 12, no. 1 (2018), 194-223
* doi:10.1214/18-EJS1391

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