Asymptotic normality of sample autocovariances with an application in frequency estimation

Asymptotic statistical properties of AR spectral estimators for processes with mixed spectra

“…More recently, [10] extended the result to the more general setting of multiple sinusoids plus colored noise with continuous spectrum. Their main result is given in Theorem 1.…”

“…Theorem 1 [10]: Given a sample of size of , and the assumptions and quantities described in Section II, then is asymptotically normal with zero mean and covariance matrix given by…”

“…That effort relied on the limiting distribution of the sample autocovariances given in [10]. In this paper, we rely on that result to develop a more concise set of limiting distributions regarding the finite-order AR modeling of a mixed spectrum process.…”

Asymptotic normality of the sample mean and covariances of evanescent fields in noise

“…Asymptotic normality of the sample covariances of linear processes was first introduced by Bartlett (see Brockwell [16] proved the asymptotic normality of the sample covariances for a time series with mixed spectra, where the observed mixed-spectrum process is the sum of a stationary process with a continuous spectra, and a finite number of real sinusoids. In, Li [15] completed the generalization of Bartlett's result to the case of complex multivariate time series with mixed spectra.…”

Asymptotically Minimum Variance Second-Order Estimation for Noncircular Signals with Application to DOA Estimation

“…and this time, the covariance matrix C s of the asymptotic distribution of s T is an Hermitian positive definite matrix thanks to its algebraic structure given by the following lemma directly deduced from [6] and [7].…”