Nonparametric estimation of large covariance matrices of longitudinal data

By Wei Biao Wu, Mohsen Pourahmadi. 2003

313 citations recorded by the source corpus.

Subfields: Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/dc0c0afe4d2033bbe49d40df8a7d4194a6142f4e

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In Management Science and Operations Research

In Statistics and Probability

Citations in the corpus

High dimensional covariance matrix estimation using a factor model (2007, unknown): “See, for example, Dempster (1972), Leonard and Hsu (1992), Chiu, Leonard and Tsui (1996), Diggle and Verbyla (1998), Pourahmadi (2000), Boik (2002), Smith and Kohn (2002), Wong, Carter and Kohn (2003), Wu and Pourahmadi (2003), Huang, Liu and Pourahmadi (2004), and Li and Gui (2005).”
Efficient Estimation in Marginal Partially Linear Models for Longitudinal/Clustered Data Using Splines (2007, methodology): “Techniques for specifying parametric covariance structure have been studied extensively in the literature (Diggle et al., 2002); non-parametric techniques have just started to emerge (Wu & Pourahmadi, 2003; Huang et al., 2006, 2007).”
HIGH-DIMENSIONAL COVARIANCE ESTIMATION BY MINIMIZING l1-PENALIZED LOG-DETERMINANT DIVERGENCE BY PRADEEP RAVIKUMAR (2009, unknown): “Submitted to the Annals of Statistics”
Positive Definite $\ell_1$ Penalized Estimation of Large Covariance Matrices (2012, methodology): “In the recent literature, regularization techniques have been used to improve the sample covariance matrix estimator, including banding (Wu and Pourahmadi, 2003; Bickel and Levina, 2008a), tapering (Furrer and Bengtsson, 2007; Cai, Zhang, and Zhou, 2010) and thresholding (Bickel and Levina, 2008b;…”
MINIMAX ESTIMATION OF LARGE COVARIANCE MATRICES UNDER ℓ1-NORM (2012, methodology): “See, for example, Wu and Pourahmadi (2003), Zou, Hastie, and Tibshirani (2006), Bickel and Levina (2008a, b), El Karoui (2008), Lam and Fan (2009), Johnstone and Lu (2009), Cai, Zhang, and Zhou (2010), and Cai and Liu (2011).”
Partial Correlation Estimation by Joint Sparse Regression Models (2008, background): “See Wu and Pourahmadi (2003), Bickel and Levina (2008), Huang et al. (2006), and Levina et al. 2008, which are all based on the modified Cholesky decomposition of the concentration matrix.”
Generalized Thresholding of Large Covariance Matrices (2009, background): “The implicit regularizing assumption here is that variables far apart are only weakly correlated, and estimators that take advantage of this have been proposed by Wu and Pourahmadi (2003) ; Bickel and Levina (2004); Huang et al. (2006); Furrer and Bengtsson (2007); Bickel and Levina (2008); Levina,”
An Overview on the Estimation of Large Covariance and Precision Matrices (2015, unknown): “For instance, in a longitudinal study where variables have a natural order, variables are likely weakly correlated when they are far apart (Wu and Pourahmadi, 2003).”
BANDING SAMPLE AUTOCOVARIANCE MATRICES OF STATIONARY PROCESSES (2009, background): “Under a short-range dependence condition for a wide class of nonlinear processes, it is shown that the banded covariance matrix estimates converge in operator norm to the true covariance matrix with explicit rates of convergence.”
Latent variable graphical model selection via convex optimization (2010, methodology): “As the sample covariance matrix is poorly behaved in such a regime, some form of regularization of the sample covariance is adopted based on assumptions about the true underlying covariance matrix [1, 2, 14, 15, 22, 39].”
An RKHS formulation of the inverse regression dimension-reduction problem (2009, background): “…for some m, the incorporation of the information in nonparametric estimation procedures may lead to a faster rate of convergence in estimating R and K [see Rice and Silverman (1991), Silverman (1996), James, Hastie and Sugar (2000), Ramsay and Silverman (2005) and Wu and Pourahmadi (2003)].”
Covariance Estimation: The GLM and Regularization Perspectives (2011, background): “Thus, one can bring the familiar regression analysis machinery to handle the unintuitive task of modeling covariance matrices (Smith and Kohn, 2002; Wu and Pourahmadi, 2003; Huang et al., 2006, Huang, Liu and Liu, 2007; Bickel and Levina, 2008a; Rothman, Levina and Zhu, 2009).”
Random matrix theory in statistics: A review (2014, methodology): “Related regularization methods have been proposed by Wu and Pourahmadi (2003, 2009).”