Nonparametric independence screening and structure identification for ultra-high dimensional longitudinal data

Abstract

Ultra-high dimensional longitudinal data are increasingly common and the analysis is challenging both theoretically and methodologically. We offer a new automatic procedure for finding a sparse semivarying coefficient model, which is widely accepted for longitudinal data analysis. Our proposed method first reduces the number of covariates to a moderate order by employing a screening procedure, and then identifies both the varying and constant coefficients using a group SCAD estimator, which is subsequently refined by accounting for the within-subject correlation. The screening procedure is based on working independence and B-spline marginal models. Under weaker conditions than those in the literature, we show that with high probability only irrelevant variables will be screened out, and the number of selected variables can be bounded by a moderate order. This allows the desirable sparsity and oracle properties of the subsequent structure identification step. Note that existing methods require some kind of iterative screening in order to achieve this, thus they demand heavy computational effort and consistency is not guaranteed. The refined semivarying coefficient model employs profile

Conditional quantile correlation learning for ultrahigh dimensional varying coefficient models and its application in survival analysis

“…Similar requirements can be found in [6,7,9] for screening in ultra-high dimensional varying coefficient models.…”

“…It has been well known that results from a single SIS procedure are rather crude (see [5,7,9,10]). In implementation, we don't directly determine threshold parameters ν n in (14) and ς n in (18) However, these approaches cannot guarantee that the selected set is exactly the same as the truly active set.…”

“…Recently, many excellent variable screening methods for nonparametric models especially for varying coefficient models were presented in the literature [6][7][8][9][10]31]. We highlight a few relevant works for the marginal varying coefficient model…”

“…Note that both [9] and [7] considered B-spline approximation for the coefficient functions, while [10] used kernel smoothing technique. In these works, the SIS properties were rigorously established.…”

Feature Screening in Ultrahigh Dimensional Generalized Varying-coefficient Models

“…For example, Li and Zhang (2011) proposed a new semiparametric threshold model for censored longitudinal data analysis. Cheng, et al (2014) offered a new automatic procedure for finding a sparse semivarying coefficient model, which is widely accepted for longitudinal data analysis. This paper intends to fill this gap.…”