Sequential estimation of high-dimensional signal plus noise models under general elliptical frameworks

Abstract

High dimensional data analysis has attracted considerable interest and is facing new challenges, one of which is the increasingly available data with noise corrupted and in a streaming manner, such as signals and stocks. In this paper, we develop a sequential method to dynamically update the estimates of signal and noise strength in signal plus noise models. The proposed sequential method is easy to compute based on the stored statistics and the current data point. The consistency and, more importantly, the asymptotic normality of the estimators of signal strength and noise level are demonstrated for high dimensional settings under mild conditions. Simulations and real data examples are further provided to illustrate the practical utility of our proposal.