Semiparametric Regression Pursuit

By Jian Huang, Fengrong Wei, Shuangge Ma. 2012

76 citations recorded by the source corpus.

The semiparametric partially linear model allows flexible modeling of covariate effects on the response variable in regression. It combines the flexibility of nonparametric regression and parsimony of linear regression. The most important assumption in the existing methods for the estimation in this model is to assume a priori that it is known which covariates have a linear effect and which do not. However, in applied work, this is rarely known in advance. We consider the problem of estimation in the partially linear models without assuming a priori which covariates have linear effects. We propose a semiparametric regression pursuit method for identifying the covariates with a linear effect. Our proposed method is a penalized regression approach using a group minimax concave penalty. Under suitable conditions we show that the proposed approach is model-pursuit consistent, meaning that it can correctly determine which covariates have a linear effect and which do not with high probability. The performance of the proposed method is evaluated using simulation studies, which support our theoretical results. A real data example is used to illustrated the application of the proposed method.

Subfields: Statistics and Probability

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In Statistics and Probability

1. Heng Lian
2. Jian Huang
3. Patrick Breheny
4. Shuangge Ma
5. Yin Lou
6. Jianyi Yang
7. Xin Chen
8. Jacob Bien

Citations in the corpus

• Sparse Partially Linear Additive Models (2014, methodology): “In [10], the authors use a group MCP penalty to decide which features should be linear versus nonlinear, but features may not be completely excluded from the model.”
• A Selective Review of Group Selection in High-Dimensional Models. (2012, methodology): “It is reasonable to use penalty functions that work well for individual variable selection.”
• Identification of Partially Linear Structure in Additive Models with an Application to Gene Expression Prediction from Sequences (2012, methodology): “In Huang, Wei, and Ma (2010), the authors used truncated power basis functions to approximate the nonlinear components; however, no variable selection is performed.”