Seminar: Estimation of the block covariance matrix with structured off-diagonal blocks

Dr Eng Monika Mokrzycka, Institute of Plant Genetics, Polish Academy of Sciences, Poznan, Poland 

Abstract:

The aim of the talk is to present the methods of covariance matrix estimation by symmetric positive definite block matrix with structured cross-covariance matrices. Such estimation is of interest for some particular data sets, which are partitioned into four sub-blocks with square diagonal blocks, not necessarily of the same order, and off-diagonal blocks being corresponding part of autoregression of order one structure. Commonly used maximum likelihood estimation in such a problem is challenging and time-consuming, thus we propose both maximum likelihood approach and method based on the least squares. Drawback on least squares method is that estimates are not always well-conditioned and may not be definite, hence we improve least squares approach by application of shrinking method.