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- Clifford Lam, Jianqing Fan
- Annals of statistics
- 2009

This paper studies the sparsistency and rates of convergence for estimating sparse covariance and precision matrices based on penalized likelihood with nonconvex penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case of applications,â€¦ (More)

- Clifford Lam, Jiangqing Fan
- Annals of statistics
- 2008

The generalized varying coefficient partially linear model with growing number of predictors arises in many contemporary scientific endeavor. In this paper we set foot on both theoretical and practical sides of profile likelihood estimation and inference. When the number of parameters grows with sample size, the existence and asymptotic normality of theâ€¦ (More)

- Clifford Lam, Qiwei Yao
- 2012

This paper deals with the factor modeling for high-dimensional time series based on a dimension-reduction viewpoint. Under stationary settings, the inference is simple in the sense that both the number of factors and the factor loadings are estimated in terms of an eigenanalysis for a non-negative definite matrix, and is therefore applicable when theâ€¦ (More)

- Clifford Lam, Qiwei Yao
- 2011

This paper deals with the dimension reduction of high-dimensional time series based on a lowerdimensional factor process. In particular we allow the dimension of time series N to be as large as, or even larger than, the length of observed time series (also refereed as the sample size) T . The estimation of the factor loading matrix and the factor processâ€¦ (More)

- Clifford Lam, Jianqing Fan
- 2007

This paper studies the sparsistency, rates of convergence, and asymptotic normality for estimating sparse covariance matrices based on penalized likelihood with non-concave penalty functions. Here, sparsistency refers to the property that all parameters that are zero are actually estimated as zero with probability tending to one. Depending on the case ofâ€¦ (More)

- Clifford Lam
- 2014

We introduce nonparametric regularization of the eigenvalues of a sample covariance matrix through splitting of the data (NERCOME), and prove that NERCOME enjoys asymptotic optimal nonlinear shrinkage of eigenvalues with respect to the Frobenius norm. One advantage of NERCOME is its computational speed when the dimension is not too large. We prove thatâ€¦ (More)

- Clifford Lam
- 2008

This paper focuses on exploring the sparsity of the inverse covariance matrix Î£ âˆ’1 , or the precision matrix. We form blocks of parameters based on each off-diagonal band of the Cholesky factor from its modified Cholesky decomposition, and penalize each block of parameters using the L 2-norm instead of individual elements. We develop a one-step estimator,â€¦ (More)

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