Analysis of multivariate non-gaussian functional data: A semiparametric latent process approach

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, transformation 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.