| 讲座简介： | We propose a model-free variable selection approach, namely constrained kernel regression. Instead of relying on model-based loss functions, the proposed approach is developed based on conditional independence relationship measured by conditional distance covariance/correlation. The conditional distance covariance/correlation is further approximated using the kernel density estimation method. The regression coefficient vector is then defined to be the vector satisfying the approximated conditional independence constraints. We prove that the proposed approach can consistently identify the true important predictor set under high-dimensional model-free settings with appropriate tuning parameters. The advantage of the proposed procedure is further shown by various numerical studies. More specifically, the proposed model-free procedure surpasses the existing model-based methods in the presence of model misspecification while outperforms or at least equates to the existing ones with correctly specified models. |
