Modeling temporally uncorrelated components of complex-valued stationary processes

Modern Stochastics: Theory and Applications

Niko Lietzén¹  Pauliina Ilmonen²  Lauri Viitasaari³ 

[1] Department of Mathematics and Statistics, University of Turku, P.O. Box 772, 00074 CGI, Finland;Department of Mathematics and Systems Analysis, Aalto University School of Science, Finland;Department of Mathematics, Uppsala University, Sweden;

关键词: Asymptotic theory;    blind source separation;    long-range dependency;    multivariate analysis;    noncentral limit theorems;   

DOI  :  10.15559/21-VMSTA190

来源: DOAJ

【 摘 要 】

A complex-valued linear mixture model is considered for discrete weakly stationary processes. Latent components of interest are recovered, which underwent a linear mixing. Asymptotic properties are studied of a classical unmixing estimator which is based on simultaneous diagonalization of the covariance matrix and an autocovariance matrix with lag τ. The main contributions are asymptotic results that can be applied to a large class of processes. In related literature, the processes are typically assumed to have weak correlations. This class is extended, and the unmixing estimator is considered under stronger dependency structures. In particular, the asymptotic behavior of the unmixing estimator is estimated for both long- and short-range dependent complex-valued processes. Consequently, this theory covers unmixing estimators that converge slower than the usual $\sqrt{T}$ and unmixing estimators that produce non-Gaussian asymptotic distributions. The presented methodology is a powerful preprocessing tool and highly applicable in several fields of statistics.

【 授权许可】

Unknown