Please use this identifier to cite or link to this item: http://scholarbank.nus.edu.sg/handle/10635/121222
Title: ESTIMATION OF LARGE-SCALE CROSS-COVARIANCE MATRIX WITH GROUP INFORMATION
Authors: TEO GUO CI
Keywords: cross covariance
Issue Date: 7-Apr-2015
Source: TEO GUO CI (2015-04-07). ESTIMATION OF LARGE-SCALE CROSS-COVARIANCE MATRIX WITH GROUP INFORMATION. ScholarBank@NUS Repository.
Abstract: SHRINKAGE ESTIMATION OF LARGE-SCALE SPARSE COVARIANCE MATRIX IS AN IMPORTANT TECHNIQUE IN THE EXPLORATORY ANALYSIS OF HIGH-DIMENSIONAL DATA SETS. WE PROPOSE A TWO-STEP PROCEDURE TO ESTIMATE LARGE-SCALE COVARIANCE MATRIX FOR ONE SET OF VARIABLES $\BX$ WITH KNOWN GROUP INFORMATION, FOLLOWED BY ESTIMATION OF COVARIANCE MATRIX BETWEEN $\BX$ AND ANOTHER SET OF VARIABLES $\BY$, DENOTED BY $\BSXX$ AND $\BSXY$ RESPECTIVELY. THE COVARIANCE MATRIX $\BSXY$ IS ESTIMATED AS THE PRODUCT OF TWO COMPONENTS, NAMELY $\BSXX \BB$. SIMILAR TO THE IDEA OF \CITET{FAN_POET}'S PRINCIPAL ORTHOGONAL COMPLEMENT THRESHOLDING (POET) ESTIMATOR, $\BSXX$ IS DECOMPOSED INTO A SYSTEMATIC FACTOR COMPONENT AND AN IDIOSYNCRATIC COMPONENT $\BSXX = \BS_{\BF F} + \BS_{\BSYM{\UPSILON}}$ IN THE FIRST STEP, WHERE THE FORMER EXPLAINS THE VARIABILITY ASSOCIATED WITH KNOWN GROUPS AND THE LATTER THE RESIDUAL VARIABILITY IN $\BX$.
URI: http://scholarbank.nus.edu.sg/handle/10635/121222
Appears in Collections:Ph.D Theses (Open)

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