报告题目: Nonparametric Screening for Additive Quantile Regression in Ultra-high Dimension

报告人：  李道纪

报告时间：2024年5月29日16：00-17：00

报告地点：文波楼202智慧教室

摘要（Abstract）: In practical applications, one often does not know the true structure of the underlying conditional quantile function, especially in the ultra-high dimensional setting. To deal with ultra-high dimensionality, quantile-adaptive marginal nonparametric screening methods have been recently developed. However, these approaches may miss important covariates that are marginally independent of the response, or may select unimportant covariates due to their high correlations with important covariates. To mitigate such shortcomings, we develop a conditional nonparametric quantile screening procedure (complemented by subsequent selection) for nonparametric additive quantile regression models. Under some mild conditions, we show that the proposed screening method can identify all relevant covariates in a small number of steps with probability approaching one. The subsequent narrowed best subset (via a modified Bayesian information criterion) also contains all the relevant covariates with overwhelming probability. The advantages of our proposed procedure are demonstrated through simulation studies and a real data example.