Functional Varying Coefficient Model with Time-independent Covariate and Longitudinal Response

Behdad Mostafaiy,Mohammad Reza Faridrohani

doi:10.6339/jds.201507_13(3).0002

Abstract

In this paper, we consider functional varying coefficient model in present of a time invariant covariate for sparse longitudinal data contaminated with some measurement errors. We propose a regularization method to estimate the slope function based on a reproducing kernel Hilbert space approach. As we will see, our procedure is easy to implement. Our simulation results show that the procedure performs well, especially when either sampling frequency or sample size increases. Applications of our method are illustrated in an analysis of a longitudinal CD4+ count dataset from an HIV study.

Highlights

In functional data, unlike multivariate data, the observations are naturally curves
We present the general definitions and common properties of reproducing kernel Hilbert space (RKHS) required in this paper
The objective here is to evaluate the effects of centred age at human immune deficiency virus (HIV) infection on CD4+ counts based on model (1)

Summary

Introduction

Unlike multivariate data, the observations are naturally curves They are independent and identically distributed realizations of a stochastic process. We want to estimate α0(t) and β0(t) in the situation that the observations are sparse and irregular longitudinal data and contaminated with some measurement errors. Let Vij denote the observations of the random function Yi at the random times Tij, contaminated with measurement errors εij which are assumed to be independent and identically distributed with means zero and finite variance, and independent of random function Y. Setup discussed above, the mean function estimate μY(t) can be obtained by, for example, any of the methods discussed in Yao et al (2005), Li and Hsing (2010), and Cai and Yuan (2011).

Estimation Method

Simulation Studies

Application