Unified statistical inference for a novel nonlinear dynamic functional/longitudinal data model

TL;DR

This paper introduces a new flexible statistical model, Semi-VCAM, for analyzing complex functional and longitudinal data, providing unified inference methods that work across different data density regimes, with applications to COVID-19 and CD4 data.

Contribution

The paper develops a novel Semi-VCAM model combining varying coefficient and additive models, along with unified asymptotic theory and testing procedures applicable to sparse, dense, and ultra-dense data.

Findings

Asymptotic theories established for a unified framework across data densities.

Proposed estimation and testing methods perform well in simulations.

Applications demonstrate the model's effectiveness on real-world COVID-19 and CD4 data.

Abstract

In light of recent work studying massive functional/longitudinal data, such as the resulting data from the COVID-19 pandemic, we propose a novel functional/longitudinal data model which is a combination of the popular varying coefficient (VC) model and additive model. We call it Semi-VCAM in which the response could be a functional/longitudinal variable, and the explanatory variables could be a mixture of functional/longitudinal and scalar variables. Notably some of the scalar variables could be categorical variables as well. The Semi-VCAM simultaneously allows for both substantial flexibility and the maintaining of one-dimensional rates of convergence. A local linear smoothing with the aid of an initial B spline series approximation is developed to estimate the unknown functional effects in the model. To avoid the subjective choice between the sparse and dense cases of the data, we establish the asymptotic theories of the resultant Pilot Estimation Based Local Linear Estimators (PEBLLE) on a unified framework of sparse, dense and ultra-dense cases of the data. Moreover, we construct unified consistent tests to justify whether a parsimony submodel is sufficient or not. These test methods also avoid the subjective choice between the sparse, dense and ultra dense cases of the data. Extensive Monte Carlo simulation studies investigating the finite sample performance of the proposed methodologies confirm our asymptotic results. We further illustrate our methodologies via analyzing the COVID-19 data from China and the CD4 data.