Analysis of Multivariate Non-Gaussian Functional Data: A Semiparametric Latent Process Approach

• Activity Number: 106 - New Statistical Models for Functional Data/ Longitudinal Data
• Type: Topic Contributed
• Date/Time: Monday, August 8, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Jiakun Jiang* and Huazhen Lin and Qingzhi Zhong and Yi Li
• Companies: Center for Statistics and Data Science, Beijing Normal University at Zhuhai and Center of Statistical Research and School of Statistics, SWUFE and Center of Statistical Research and School of Statistics, SWUFE and Department of Biostatistics, University of Michigan
• Keywords: Functional regression analysis; latent process ; semiparametric

Abstract

Commonly assumed for multivariate functional regression models are normality and structural dependence, which, however, may not hold in practice. To relax these restrictions, we propose a new semiparametric transformation latent process functional regression model for multivariate functional data. Our model does not require normality assumptions or any specific dependence structures among multivariate response curves or intra-individual variability across time. We propose a combined likelihood- and estimating equation-based method to estimate parameters, trans- formation functions and covariance structures. We establish theoretical properties, including ?n?consistency and asymptotic normality, for the proposed estimators. The utility of the method is illustrated via extensive simulations and analyses of an elderly cognitive evolution dataset, which yield a better fit than the other competing methods and some interesting findings.