Project B4: Bayesian nonparametric adaptive estimation of Toeplitz covariance matrices

Estimation of the covariance matrix of a vector Y with a known mean is a central problem in many areas of multivariate analysis and is a complex task.

In this project we would like to exploit the idea to estimate the covariance matrix of a stationary process based on the single realisation of length n from its spectral density. Thereby, we aim to employ a Bayesian framework and impose smoothness on the spectral density by an appropriate prior. The asymptotic properties of the resulting estimators are to be studied.

Subsequently, the method should be extended to the case of the unkknown mean.

Methods: Bayesian estimation, spline smoothers, Fourier series, trigonometric approximation
Applications: estimation, inference and dimension reduction for dependent data