Variance Estimation Based on Invariance Principles

Abstract

Consistent variance estimators for certain stochastic processes are suggested using the fact that (weak or strong) invariance principles may be available. Convergence rates are also derived, the latter being essentially determined by the approximation rates in the corresponding invariance principles. As an application, a change point test in a simple AMOC renewal model is briefly discussed, where variance estimators possessing good enough convergence rates are required.

Keywords:

• AMS 1991 subject classification
• Primary 62G05
• secondary 62G20
• 60F17

Keywords:

• consistent variance estimation
• invariance principle
• Wiener process
• renewal process
• convergence rate
• extreme value asymptotics
• change point problem
• increments of Wiener processes