CHINESE JOURNAL OF APPLIED PROBABILITY AND STATIST 2015, 31(4) 347-356 DOI:      ISSN: 1001-4268 CN: 31-1256

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General Shrinkage Rule with Respect to gamma-Norms for Bridge Estimation

Gai Yujie, Zhang Zhanli, Zhang Jun

School of Statistics and Mathematics, Central University of Finance and Economics; Shen Zhen -- Hong Kong Joint Research Centre for Applied Statistical Sciences, College of Mathematics and Computational Science, Institute of Statistical Sciences, Shenzhen University

Abstract��

Bridge regression, a special family of penalized regressions
of a penalty function $\fn_jvn \100dpi \inline \tsm|\beta_j|^\gamma$ with $\fn_jvn \100dpi \inline \gamma>0$, has been studied in many
literatures. In this paper, we provide some theoretical results of how the shrinkage
rule changing with $\fn_jvn \100dpi \inline \gamma$ under two settings: $\fn_jvn \100dpi \inline \gamma\geq 1$ and $\fn_jvn \100dpi \inline 0<\gamma<1$,
respectively. Simulation results are conducted to evaluate the performance of the
proposed method.

Keywords��