Simultaneous structure estimation and variable selection in partial linear varying coefficient models for longitudinal data

Abstract

Partial linear varying coefficient models (PLVCM) are often considered for analysing longitudinal data for a good balance between flexibility and parsimony. The existing estimation and variable selection methods for this model are mainly built upon which subset of variables have linear or varying effect on the response is known in advance, or say, model structure is determined. However, in application, this is unreasonable. In this work, we propose a simultaneous structure estimation and variable selection method, which can do simultaneous coefficient estimation and three types of selections: varying and constant effects selection, relevant variable selection. It can be easily implemented in one step by employing a penalized M-type regression, which uses a general loss function to treat mean, median, quantile and robust mean regressions in a unified framework. Consistency in the three types of selections and oracle property in estimation are established as well. Simulation studies and real data analysis also confirm our method.

Keywords:

• longitudinal data
• partial linear varying coefficient models
• three types of selections
• selection consistency
• oracle property

Mathematics Subject Classification::

• 62G05
• 62E20
• 62J02

Funding

This work was supported by NNSF project [11171188, 11231005 and 71271227] of China; Mathematical Finance-Backward Stochastic Analysis and Computations in Financial Risk Control of China [11221061]; NSF and SRRF projects [ZR2010AZ001 and BS2011SF006] of Shandong Province of China.