Quantile adaptive feature screening for ultra-high dimensional longitudinal heterogeneous data
摘要
In this paper, we consider the feature screening problem of ultra-high dimensional longitudinal heterogeneous data, which significantly extends the existing frameworks on ultra-high dimensional heterogeneous data and ultra-high dimensional longitudinal data focusing only on mean regression. A quantile adaptive feature screening approach is proposed by integrating independence screening with quadratic inference functions (QIF). This framework offers two distinctive features: (1) it takes into account the within-subject dependency and is more efficient than that of ignoring the correlation and assuming independence for each subject; (2) it allows the set of active variables to vary with different quantiles, thereby providing a more comprehensive description for the real data and flexibility to accommodate heterogeneity. The sure screening property is shown under some regularity conditions. Some simulation studies and a real data analysis are conducted to assess the effectiveness of the proposed screening method. The numerical results indicate that the proposed method is an effective tool to handle with the ultra-high dimensional longitudinal data.