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

TL;DR

This paper establishes a uniform convergence law for additive functionals of partial sum processes to the local times of linear fractional stable motions, aiding statistical analysis involving these processes.

Contribution

It introduces a general uniform law for weak convergence to local times of linear fractional stable motions, applicable in statistical modeling.

Findings

Provides a fundamental tool for analyzing nonparametric estimators involving such processes.

Enables rigorous statistical inference for models with linear fractional stable motions.

Facilitates understanding of the global properties of nonlinear statistical models.

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.