CLT for Nonlinear Shrinkage Estimators of Large Covariance Matrices

This thesis is concerned with finding the asymptotic distributions of linear spectral statistics of the nonlinear shrinkage estimator for large covariance matrices derived by Ledoit and Wolf (2012). It provides some new inferential procedures for large-dimensional data and shed some light on the power of the new statistical tests on the...

Central Limit Theorems for Linear Spectral Statistics on Large Regularized Covariance Matrices

In this thesis we shall consider sample covariance matrices Sn in the case when the dimension of the data increases with the sample size to infinity ,while the ratio approaches a fixed constant. We will derive a new statistic based on the general linear shrinkage estimator by Bodnar et al. (2014)[1] We will show that the new statistic is...

Uncertainty analysis in determining the position of a drill bit with the covariance method

During oil drilling, the position of wells is indirectly determined by measurements near the drilling bit. However, the measurements are disturbed by noise causing errors in the measurements. It is important for large oil companies like Shell to determine the position of wells with a certain degree of uncertainty. Therefore, the main objective...