Translator Disclaimer
December 2012 Asymptotic properties of the approximate inverse estimator for directional distributions
M. Riplinger, M. Spiess
Author Affiliations +
Adv. in Appl. Probab. 44(4): 954-976 (December 2012). DOI: 10.1239/aap/1354716585

Abstract

For stationary fiber processes, the estimation of the directional distribution is an important task. We consider a stereological approach, assuming that the intersection points of the process with a finite number of test hyperplanes can be observed in a bounded window. The intensity of these intersection processes is proportional to the cosine transform of the directional distribution. We use the approximate inverse method to invert the cosine transform and analyze asymptotic properties of the estimator in growing windows for Poisson line processes. We show almost-sure convergence of the estimator and derive Berry--Esseen bounds, including formulae for the variance.

Citation

Download Citation

M. Riplinger. M. Spiess. "Asymptotic properties of the approximate inverse estimator for directional distributions." Adv. in Appl. Probab. 44 (4) 954 - 976, December 2012. https://doi.org/10.1239/aap/1354716585

Information

Published: December 2012
First available in Project Euclid: 5 December 2012

zbMATH: 1275.62043
MathSciNet: MR3052845
Digital Object Identifier: 10.1239/aap/1354716585

Subjects:
Primary: 60G10
Secondary: 60D05

Rights: Copyright © 2012 Applied Probability Trust

JOURNAL ARTICLE
23 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
Vol.44 • No. 4 • December 2012
Back to Top