Estimation of integrated squared spectral density derivatives

Abstract

Kernel spectrum estimates are used for the estimation of integrals of various squared derivatives of a spectral density. Rates of convergence in mean squared error are calculated, which show that the parametric rate of convergence n-1 can be achieved with some smoothness conditions on the spectral density function. The implications for data-driven bandwidth selection in kernel spectral density estimation are considered.Integrated squared derivative kernel spectrum estimate rate of convergence