Sparse bridge estimation with a diverging number of parameters

作者：Kwon Sunghoon; Kim Yongdai; Choi Hosik^*

来源：Statistics and Its Interface, 2013, 6(2): 231-242.

DOI：10.4310/sii.2013.v6.n2.a7

• Bridge
• Diverging number of parameters
• Lasso
• Regression
• Ridge
• Variable selection

The Bridge estimator with l(nu)(nu)-penalty for some nu > 0 is one of the popular choices in penalized linear regression models. It is known that, when nu <= 1, the Bridge estimator produces sparse models which allow us to control the model complexity. However, when nu = 1, the Bridge estimator fails to identify the correct model since it requires certain strong sufficient conditions that are hard to hold in general, and when nu > 1, it achieves no sparsity in parameter estimation. In this paper, we propose the sparse Bridge estimator that is developed to find the correct sparse version of the Bridge estimator when nu >= 1. Theoretically, the sparse Bridge estimator is asymptotically equivalent to the oracle Bridge estimator when the number of predictive variables diverges to infinity but less than the sample size. Here, the oracle Bridge estimator is an ideal Bridge estimator obtained by deleting all irrelevant predictive variables in advance. Hence, the sparse Bridge estimator naturally inherits the properties of the Bridge estimator without losing correct model identification asymptotically. Numerical studies show that the sparse Bridge estimator can outperform other penalized estimators with a finite sample.

• 出版日期2013