Variable Selection in Kernel Regression Using Measurement Error Selection Likelihoods

• 成果类型: Article
• 署名作者: White, Kyle R.; Stefanski, Leonard A.; Wu, Yichao
• 署名单位: North Carolina State University; University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1222287
• 发表日期: 2017
• 页码: 1587-1597
• 关键词: Nonparametric regression; simulation-extrapolation; noise injection; splines; models; SPARSE

摘要

This article develops a nonparametric shrinkage and selection estimator via the measurement error selection likelihood approach recently proposed by Stefanski, Wu, and White. The measurement error kernel regression operator (MEKRO) has the same form as the Nadaraya-Watson kernel estimator, but optimizes a measurement error model selection likelihood to estimate the kernel bandwidths. Much like LASSO or COSSO solution paths, MEKRO results in solution paths depending on a tuning parameter that controls shrinkage and selection via a bound on the harmonic mean of the pseudo-measurement error standard deviations. We use small-sample-corrected AIC to select the tuning parameter. Large-sample properties of MEKRO are studied and small-sample properties are explored via Monte Carlo experiments and applications to data. Supplementary materials for this article are available online.