Statistics – Applications
Scientific paper
2009-08-14
Annals of Applied Statistics 2009, Vol. 3, No. 2, 521-541
Statistics
Applications
Published in at http://dx.doi.org/10.1214/08-AOAS215 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Ins
Scientific paper
10.1214/08-AOAS215
Graphical models are frequently used to explore networks, such as genetic networks, among a set of variables. This is usually carried out via exploring the sparsity of the precision matrix of the variables under consideration. Penalized likelihood methods are often used in such explorations. Yet, positive-definiteness constraints of precision matrices make the optimization problem challenging. We introduce nonconcave penalties and the adaptive LASSO penalty to attenuate the bias problem in the network estimation. Through the local linear approximation to the nonconcave penalty functions, the problem of precision matrix estimation is recast as a sequence of penalized likelihood problems with a weighted $L_1$ penalty and solved using the efficient algorithm of Friedman et al. [Biostatistics 9 (2008) 432--441]. Our estimation schemes are applied to two real datasets. Simulation experiments and asymptotic theory are used to justify our proposed methods.
Fan Jianqing
Feng Yangyue
Wu Yichao
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