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Activity Number: 171 - New Nonparametric Methods for Correlated Data
Type: Contributed
Date/Time: Monday, July 30, 2018 : 10:30 AM to 12:20 PM
Sponsor: Section on Nonparametric Statistics
Abstract #328844
Title: Ultra-High-Dimensional Single-Index Models for Longitudinal Data
Author(s): Brittany Green* and Yan Yu and Dr. LIAN Heng
Companies: University of Cincinnati and University of Cincinnati and City University of Hong Kong
Keywords: GEE; Oracle properties; Polynomial splines; SCAD; Variable Selection
Abstract:

Problems involving potentially ultra-high-dimensional longitudinal data are growing in importance in fields such as genomics and large-scale public health studies. We investigate flexible models for ultra-high dimensional longitudinal data where nonlinearity is present. Variable selection and estimation are challenging in this problem due to the large number of predictor variables, nonlinear relationship, and the complexities of longitudinal data. We propose using generalized estimating equations and partially linear single-index models to capture the nonlinearity among predictors for correlated data, avoiding the "curse of dimensionality." We adopt B-splines to approximate the unknown function. We propose an efficient algorithm through linear approximation. Large sample properties are established along with oracle properties for variable selection via SCAD. Simulation studies and a real data application demonstrate success of our method.


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