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.