On estimation in varying coefficient models for sparse and irregularly sampled functional data

TL;DR

This paper introduces a smoothness regularization approach for estimating varying coefficient models from sparse, irregular, and noisy functional data, using RKHS methods to improve covariance estimation and coefficient function fitting.

Contribution

It presents a novel regularization-based estimation method for varying coefficient models tailored to sparse, irregular, and error-contaminated functional data, with demonstrated effectiveness.

Findings

The proposed method accurately estimates covariance functions.

Simulation studies show good performance of the approach.

Application to real data illustrates practical utility.

Abstract

In this paper, we study a smoothness regularization method for a varying coefficient model based on sparse and irregularly sampled functional data which is contaminated with some measurement errors. We estimate the one-dimensional covariance and cross-covariance functions of the underlying stochastic processes based on a reproducing kernel Hilbert space approach. We then obtain least squares estimates of the coefficient functions. Simulation studies demonstrate that the proposed method has good performance. We illustrate our method by an analysis of longitudinal primary biliary liver cirrhosis data.