Variable Selection in Kernel Regression Using Measurement Error Selection Likelihoods
本文提出一种非参数收缩与选择估计量MEKRO，通过测量误差模型选择似然估计核带宽，实现变量选择，并用小样本校正AIC选择调优参数，适用于高维数据建模。
This paper 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.