Convergence rate of plugin estimates for functional parameters with applications to locally-stationary time-series

Abstract

Some distribution parameter estimates depend on nuisance parameters, and it is a common practice to plug in their estimates. The convergence properties of the resulting estimate are of interest. We consider the case where both estimators – the one plugged in, and its recipient – are random quantities, while literature covers mostly plugin to a deterministic function. We present a way of computing this final convergence rate, based on the convergence rate of a nonrandom, but perturbed quantity plugged in. The theoretical result is applied to the construction of simultaneous confidence band for auto-correlation functions of a locally-stationary time series.