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

Abstract

Studying massive functional/longitudinal data, we adopt a flexible nonlinear dynamic regression method named the Semi-Varying Coefficient Additive Model, in which the response can be a functional/longitudinal variable, and the explanatory variables can be a mixture of functional/longitudinal and scalar variables. With the aid of an initial B-spline approximation, a local linear smoothing is proposed to estimate the unknown functional effects in the model. Existing methods of statistical inference for sparse data and dense data are significantly different. We therefore develop 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 data. Remarkably, we obtain the oracle properties as if other functions were known in advance. Extensive Monte Carlo simulation studies investigating the finite sample performance of the proposed methodologies confirm our asymptotic results. We further illustrate our methodologies by analyzing COVID-19 data from China.