Estimation of a clustering model for non Gaussian functional data

Abstract

Model-based clustering analysis of functional data often has normality assumption. This article considers clustering non Gaussian functional data. We propose a novel non Gaussian functional mixed-effects model without the prior information and clustering number. We use transformation functions to accommodate non Gaussian functional data. Smoothing spline ANOVA and cubic B-spline approximate unknown fixed effects and random effects, respectively. A penalized likelihood is used to estimate unknown parameters, and the consistency and asymptotic normality is provided after that. We take simulations for different measurement error distribution assumptions and adopt the air quality of Italian city data. Both simulation and actual data analysis show that the proposed method performs well and has a better clustering effect.

KEYWORDS:

• Clustering analysis
• non Gaussian functional data
• transformation function
• smoothing spline ANOVA
• penalized likelihood

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by the National Natural Science Foundation of China (11971171,11831008,12171310), and the Basic Research Project of Shanghai Science and Technology Commission (22JC1400800).