Covariance matrix selection and estimation via penalised normal likelihood

By Jianhua Z. Huang, N. Liu, Mohsen Pourahmadi, Linxu Liu. 2006

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Citations in the corpus

Nonparametric Independence Testing for Small Sample Sizes (2014, background): “Over the decades, there have been many estimators proposed for covariance matrices that outperform the sample covariance matrix in different situations - see [10, 11, 12, 13].”
Covariance and precision matrix estimation for high-dimensional time series (2013, methodology): “Other estimates include the Cholesky decomposition based method [Wu and Pourahmadi (2003), Huang et al. (2006)], neighborhood selection for sparse graphical models [Liu and Luo (2012), Yuan (2010), Meinshausen and Bühlmann (2006)], regularized likelihood approach [Lam and Fan (2009), Fan, Feng and W”
Two Sample Tests for High Dimensional Covariance Matrices (2012, unknown): “) and Lam, Yao and Bathia (2011) considered covariance estimation under factor models. There are also developments in conducting LASSO-type regularization estimation of highdimensional covariances in Huang et al. (2006) and Rothman, Levina and Zhu (2010). Despite these developments, it is still chal”
Estimating structured high-dimensional covariance and precision matrices: Optimal rates and adaptive estimation (2016, background): “…Schatten norm, spectral norm, tapering, thresholding Disciplines Physical Sciences and Mathematics This journal article is available at ScholarlyCommons: https://repository.upenn.edu/statistics_papers/78 Electronic Journal of Statistics Vol. 10 (2016) 1–59 ISSN: 1935-7524 DOI: 10.1214/15-EJS1081”
Multitask Quantile Regression under the Transnormal Model (2016, methodology): “Models 1–3 are autoregressive models considered by Huang et al. (2006) and Xue and Zou (2012).”
Informative Estimation and Selection of Correlation Structure for Longitudinal Data (2012, methodology): “…on the estimation of the covariance matrix rather than on the selection of correlation structure, including the Cholesky decomposition approach (Huang et al. 2006; Huang, Liu, and Liu 2007), the factor modeling approach (Fan, Fan, and Lv 2008), and the spectrum random matrix approach (El…”
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).”
Monitoring the covariance matrix via penalized likelihood estimation (2013, methodology): “Huang et al. (2006) developed a data-driven method to identify parsimony in the covariance matrix. Based on the modified Cholesky decomposition proposed by Pourahmadi (1999, 2000), the authors proposed to add L1 or L2 penalties to the normal likelihood in order to shrink the off-diagonal elements to”
Nonparametric eigenvalue-regularized precision or covariance matrix estimator (2016, methodology): “We analyze the call center data considered in Huang et al. (2006) and Bickel and Levina (2008b).”
Maximum Lq-likelihood estimation. (2010, background): “d is positive otherwise. Moreover, the loss is invariant to the transformations AΣAT and AΣbqAT for a nonsingular matrix A. The use of such a loss function is common in literature (e.g., Huang et al. [17]). In Table 3, we show simulation results for moderate or small sample sizes ranging from 10 to ”
Partial Correlation Estimation by Joint Sparse Regression Models (2008, methodology): “…methods have also been proposed for selecting the tuning parameter in the setting of covariance estimation, for example, the MSE based criterion in Schafer and Strimmer (2005), the likelihood based method in Huang et al. (2006), and the cross-validation and bootstrap methods in Li and Gui (2006).”
Covariance regularization by thresholding (2009, methodology): “These methods use the fact that the entries of the Cholesky factor have a regression interpretation, which allows application of regression regularization tools such as the lasso and ridge penalties [21], or the nested lasso penalty [28] speciﬁcally designed for the ordered variables situation.”
Non-Concave Penalized Likelihood with NP-Dimensionality (2009, background): “See, for example, Huang et al. (2006), Meinshausen and B¨uhlmann (2006), Levina et al. (2008), Rothman et al. (2008), and Lam and Fan (2009), among others.”
HIGH-DIMENSIONAL COVARIANCE ESTIMATION BY MINIMIZING l1-PENALIZED LOG-DETERMINANT DIVERGENCE BY PRADEEP RAVIKUMAR (2009, unknown): “Submitted to the Annals of Statistics”
High dimensional covariance matrix estimation using a factor model (2007, unknown): “Huang, Liu and Pourahmadi (2004) , and Li and Gui (2005).”
Wishart distributions for decomposable covariance graph models (2011, unknown): “ that for every 1≤i≤msuch that N≺(i)6= φ,Σican be partitioned as Σi= Σ≺i Σ≺ ·i (Σ≺ ·i) T Σ ii . Also, note that if Z∼ N(0,Σ),then Dii is the conditional variance of Zi given Z1,Z2,...,Zi−1 (see [16]). Note that Σkl= 0 for all 1 ≤ k,l≤ i,k∈ N≺(i),l/∈ N≺(i). It follows that Dii= Σii− (Σ≺ ·i) T(Σ≺i)−”