RT Dissertation/Thesis
T1 New estimation methods for high dimensional inverse covariance matrices
A1 Avagyan, Vahe
AB The estimation of inverse covariance matrix (also known as precision matrix)is an important problem in various research fields and methodologies, especiallyin the current age of high-dimensional data abundance. In addition,the classical estimation methods are no longer stable and applicable in highdimensional settings, i.e., when the dimensionality has the same order as thesample size or is much larger.This thesis focuses on the estimation of the precision matrices as well as theirapplications. In particular, the goal of this thesis is to develop and analyseaccurate precision matrix estimators for problems in high-dimensional settings.Moreover, the proposed precision matrix estimators should emulatethe existing prominent estimators in terms of different statistical measureswithout being computationally more extensive.This thesis is comprised of two articles on estimation of precision matricesin high dimensional settings. In what follows, we summarize the maincontributions of this thesis.First, we propose a simple improvement of the popular Graphical LASSO(GLASSO) framework that is able to attain better statistical performancewithout increasing signi cantly the computational cost. The proposed improvementis based on computing a root of the sample covariance matrixto reduce the spread of the associated eigenvalues. Through extensive numericalresults, using both simulated and real datasets, we show that theproposed modiffication improves the GLASSO procedure. Our results revealthat the square-root improvement can be a reasonable choice in practice.Second, we introduce two adaptive extensions of the recently proposed l1norm penalized D-trace loss minimization method. It is well known that thel1 norm penalization often fails to control the bias of the obtained estimatorbecause of its overestimation behavior. Our proposed extensions are basedon the adaptive and weighted adaptive thresholding operators and intend todiminish the bias produced by the l1 penalty term. We present the algorithm for solving our proposed approaches, which is based on the alternating directionmethod. Extensive numerical results, using both simulated and realdatasets, show the advantage of our proposed estimators.
YR 2016
FD 2016-01
LK https://hdl.handle.net/10016/22692
UL https://hdl.handle.net/10016/22692
LA eng
DS e-Archivo
RD 20 may. 2024