Data-Driven Choice of a Spectrum Estimate: Extending the Applicability of Cross-Validation Methods

Abstract

I develop methods of objectively choosing a spectrum estimate from a general class C of available estimates. C can, for example, simultaneously include Blackman—Tukey and autoregressive estimates, so the statistician no longer needs to choose one type or the other arbitrarily. The methods work by extending the applicability of existing cross-validatory techniques through the introduction of generalized leave-out-one spectrum estimates. As special cases, I obtain new objective smoothness parameter selection methods for both autoregressive and Blackman—Tukey estimates. In a Monte Carlo study, I demonstrate the effectiveness of the particular methods that result from generalizing Wahba's CVMSE.