Asymptotic statistical properties of the Capon MV spectral estimator for mixed spectrum processes

The mixed spectrum process is used to model various periodic phenomena. The Capon power spectrum of a mixed spectrum process is useful in the estimation of the periodic component of the process. In 1994 Li et al developed the large sample statistics of the lagged-product covariance estimator for mixed processes. In this paper we use δ-method and Li´s result to derive the large sample distribution of the nth order Capon spectral estimator. Based on a number of simulations, we investigate the properties of the Capon estimator through examples. We propose two conjectures regarding the limit value of the asymptotic variance as order n goes to ∞. This leads to the speculation that the relative error of Capon estimator for large sample size and large order is inversely proportional to the square root of the local signal to noise ratio