高维线性回归模型中非凸惩罚岭回归

Combination of Nonconvex Penalties and Ridge Regression for High-Dimensional Linear Models

中文关键词:  高维  非凸惩罚  Oracle性质  岭回归  变量选择.

英文关键词:high dimension  nonconvex penalties  oracle property  ridge regression  variable selection.

中文摘要:

      非凸惩罚函数包括SCAD惩罚和MCP惩罚, 这类惩罚函数具有无偏性、连续性和稀疏性等特点，岭回归方法能够很好的克服共线性问题. 本文将非凸惩罚函数和岭回归方法的优势结合起来(简记为 NPR),研究了自变量间存在高相关性问题时NPR估计的Oracle性质. 这里主要研究了参数个数$p_n$ 随样本量$n$ 呈指数阶增长的情况. 同时, 通过模拟研究和实例分析进一步验证了NPR 方法的表现.

英文摘要:

      Nonconvex penalties including the smoothly clipped absolute deviation penalty and the minimax concave penalty enjoy the properties of unbiasedness, continuity and sparsity, and the ridge regression can deal with the collinearity problem. Combining the strengths of nonconvex penalties and ridge regression (abbreviated as NPR), we study the oracle property of the NPR estimator in high dimensional settings with highly correlated predictors, where the dimensionality of covariates $p_n$ is allowed to increase exponentially with the sample size $n$. Simulation studies and a real data example are presented to verify the performance of the NPR method.