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WROCŁAW UNIVERSITY
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Contents of PMS, Vol. 43, Fasc. 1,
pages 23 - 39
DOI: 10.37190/0208-4147.00091
Published online 14.4.2023
 

Estimation by Stable Motions and its Applications

A. Das
M. Denker
A. Levina
L. Tabacu

Abstract:

We propose a family of confidence intervals for nonparametric moment estimators if the observations have large or infinite variances. The theoretical underpinnings which guarantee the soundness of the method are demonstrated. Extensive numerical simulations show its superiority over bootstrap and normal approximation and its wide applicability. Finally, a confidence interval to estimate the coupling strength in neuronal networks is proposed.

2010 AMS Mathematics Subject Classification: Primary 62G05; Secondary 62E17, 62G09, 62G15, 60H05.

Keywords and phrases: stochastic integral, stable motion, moment estimator, U-statistics, neural avalanches.

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