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- Jinchi Lv
- 2006

High dimensionality is a growing feature in many areas of contemporary statistics. Variable selection is fundamental to high-dimensional statistical modeling. For problems of large or huge scale pn, computational cost and estimation accuracy are always two top concerns. In a seminal paper, Candes and Tao (2007) propose a minimum l1 estimator, the Dantzig… (More)

- Jianqing Fan, Jinchi Lv
- 2008

High dimensionality is a growing feature in many areas of contemporary statistics. Variable selection is fundamental to high-dimensional statistical modeling. For problems of large or huge scale pn, computational cost and estimation accuracy are always two top concerns. In a seminal paper, Candes and Tao (2007) propose a minimum l1 estimator, the Dantzig… (More)

- Jianqing Fan, Jinchi Lv
- Statistica Sinica
- 2010

High dimensional statistical problems arise from diverse fields of scientific research and technological development. Variable selection plays a pivotal role in contemporary statistical learning and scientific discoveries. The traditional idea of best subset selection methods, which can be regarded as a specific form of penalized likelihood, is… (More)

High dimensionality comparable to sample size is common in many statistical problems. We examine covariance matrix estimation in the asymptotic framework that the dimensionality p tends to∞ as the sample size n increases. Motivated by the Arbitrage Pricing Theory in finance, a multi-factor model is employed to reduce dimensionality and to estimate the… (More)

- Jinchi Lv, Yingying Fan
- 2009

Model selection and sparse recovery are two important problems for which many regularization methods have been proposed. We study the properties of regularization methods in both problems under the unified framework of regularized least squares with concave penalties. For model selection, we establish conditions under which a regularized least squares… (More)

- Jianqing Fan, Jinchi Lv
- IEEE Transactions on Information Theory
- 2011

Penalized likelihood methods are fundamental to ultrahigh dimensional variable selection. How high dimensionality such methods can handle remains largely unknown. In this paper, we show that in the context of generalized linear models, such methods possess model selection consistency with oracle properties even for dimensionality of nonpolynomial (NP) order… (More)

We propose a new algorithm, DASSO, for fitting the entire coefficient path of the Dantzig selector with a similar computational cost to the LARS algorithm that is used to compute the Lasso. DASSO efficiently constructs a piecewise linear path through a sequential simplex-like algorithm, which is remarkably similar to LARS. Comparison of the two algorithms… (More)

High-dimensional sparse modeling with censored survival data is of great practical importance, as exemplified by modern applications in high-throughput genomic data analysis and credit risk analysis. In this article, we propose a class of regularization methods for simultaneous variable selection and estimation in the additive hazards model, by combining… (More)

- Zemin Zheng, Yingying Fan, Jinchi Lv
- 2014

High dimensional sparse modelling via regularization provides a powerful tool for analysing large-scale data sets and obtaining meaningful interpretable models.The use of nonconvex penalty functions shows advantage in selecting important features in high dimensions, but the global optimality of such methods still demands more understanding.We consider… (More)

- Yingying Fan, Jinchi Lv
- 2013

High-dimensional data analysis has motivated a spectrum of regularization methods for variable selection and sparse modeling, with two popular methods being convex and concave ones. A long debate has taken place on whether one class dominates the other, an important question both in theory and to practitioners. In this article, we characterize the… (More)