2015/02/28 by Jinyuan Chang, Cheng Yong Tang, Yichao Wu · 30 citations
Computer Science · Mathematics · #Bayesian Methods and Mixture Models #Curse of dimensionality #Explanatory power #Feature (linguistics) #Identification (biology) #Independence (probability theory) #Morphological variations and asymmetry #Nonparametric regression #Nonparametric statistics #Parametric statistics #Regression analysis #Semiparametric regression #Statistical Methods and Inference #math.ST #stat.TH
paper · pdf · doi:10.1214/15-aos1374
published in The Annals of Statistics 44(2), 515-539 (Institute of Mathematical Statistics) · Published at http://dx.doi.org/10.1214/15-AOS1374 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
openalex publication_date 2016/03/23 · arxiv created 2016/03/30 · arxiv updated 2016/03/31 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We consider an independence feature screening technique for identifying explanatory variables that locally contribute to the response variable in high-dimensional regression analysis. Without requiring a specific parametric form of the underlying data model, our approach accommodates a wide spectrum of nonparametric and semiparametric model families. To detect the local contributions of explanatory variables, our approach constructs empirical likelihood locally in conjunction with marginal nonparametric regressions. Since our approach actually requires no estimation, it is advantageous in scenarios such as the single-index models where even specification and identification of a marginal model is an issue. By automatically incorporating the level of variation of the nonparametric regression and directly assessing the strength of data evidence supporting local contribution from each explanatory variable, our approach provides a unique perspective for solving feature screening problems. Theoretical analysis shows that our approach can handle data dimensionality growing exponentially with the sample size. With extensive theoretical illustrations and numerical examples, we show that the local independence screening approach performs promisingly.