Shrinkage Tuning Parameter Selection with a Diverging number of Parameters

Abstract

Contemporary statistical research frequently deals with problems involving a diverging number of parameters. For those problems, various shrinkage methods (e.g. the lasso and smoothly clipped absolute deviation) are found to be particularly useful for variable selection. Nevertheless, the desirable performances of those shrinkage methods heavily hinge on an appropriate selection of the tuning parameters. With a fixed predictor dimension, Wang and co-worker have demonstrated that the tuning parameters selected by a Bayesian information criterion type criterion can identify the true model consistently. In this work, similar results are further extended to the situation with a diverging number of parameters for both unpenalized and penalized estimators. Consequently, our theoretical results further enlarge not only the scope of applicabilityation criterion type criteria but also that of those shrinkage estimation methods. Copyright (c) 2008 Royal Statistical Society.

A Semiparametric Regression Model for Longitudinal Data with Non‐stationary Errors

“…LetS c and S v be estimated index sets of S c and S v respectively. Then, repeating (10) and (11) Another key problem in the implementation is the choice of tuning parameters λ 1 , λ 2 and λ 3 , for which many approached have been developed, see e.g., ), Wang et al (2008 and Wang et al (2009). We use the Bayesian information criterion (BIC) for its finite sample performances (see, e.g.…”

“…A recent line of research for variable selection has also undergone rapid development, see e.g., Fan & Li (2001), Wang et al (2009, Ma et al (2013). Among these studies, a working correlation model for the variance is often assumed.…”

Lasso Maximum Likelihood Estimation of Parametric Models with Singular Information Matrices

“…For least square shrinkage methods, the generalized cross validation (GCV) and information criteria such as the Akaike information criterion (AIC) and Bayesian information criterion (BIC) are often used. While the GCV and AIC cannot identify the true model consistently , the BIC can (Wang and Leng 2007;Wang et al 2009). Zhang et al (2010) propose a general information criterion (GIC) that can nest the AIC and BIC and show its consistency in model selection.…”

Selection consistency of EBIC for GLIM with non-canonical links and diverging number of parameters

“…Bogdan et al (2004) considered a criterion called modified BIC (mBIC) for QTL mapping models. Wang et al (2009) studied another modified BIC for models with a diverging number of parameters. Chen and Chen (2008) extended the original BIC to a family called extended BIC (EBIC) governed by a parameter γ.…”

“…The criterion considered by Wang et al (2009) modifies the original BIC by multiplying the second term of BIC with a diverging parameter and is somehow ad hoc. To achieve selection consistency, it requires p/n ξ < 1 for some 0 < ξ < 1, and hence is not applicable when p > n. The mBIC and EBIC considered by Bogdan et al (2004) and Chen and Chen (2008) respectively are developed from a Bayesian framework.…”