How can we discern whether the covariance operator of a stochastic process is reduced rank, and if so, what its precise rank is? And how do so at given level confidence? This question central to great deal methods for functional data, which require low-dimensional representations by PCA or other methods. The difficulty that determination be made on basis i.i.d. replications observed discretely ...

Abstract—The Maximum entropy principle in spectral analysis was used as an estimator of Direction of Arrival (DoA) of electromagnetic or acoustic sources impinging on an array of sensors, indeed the maximum entropy operator is very efficient when the signals of the radiating sources are ergodic and complex zero mean random processes which is the case for cosmic sources. In this paper, we presen...

If two wide sense stationary time series are correlated then one can be used to predict the other. The reduced rank Wiener filter is the rank constrained linear operator which maps the current value of one time series to an estimate of the current value of the other time series in an optimal way. A closed form solution exists for the reduced rank Wiener filter. This paper studies the problem of...