A uniform law for convergence to the local times of linear fractional stable motions

Abstract

We provide a uniform law for the weak convergence of additive functionals of partial sum processes to the local times of linear fractional stable motions, in a setting sufficiently general for statistical applications. Our results are fundamental to the analysis of the global properties of nonparametric estimators of nonlinear statistical models that involve such processes as covariates.

Published at http://dx.doi.org/10.1214/14-AAP1085 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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• Nonparametric estimation in a nonlinear cointegration type model
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Cited by in corpus (1)

• Uniform convergence rates over maximal domains in structural nonparametric cointegrating regression