Variance estimation based on invariance principles. (English) Zbl 0863.62073
Summary: 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.
MSC:
| 62M05 | Markov processes: estimation; hidden Markov models |
| 62G20 | Asymptotic properties of nonparametric inference |
| 60F17 | Functional limit theorems; invariance principles |
| 62G05 | Nonparametric estimation |
Keywords:
consistent variance estimation; renewal process; extreme value asymptotics; increments of Wiener processes; invariance principles; change point test; AMOC renewal model; convergence ratesReferences:
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