[HSW18] SFLM: A mix of a Functional Linear Model and of a Spatial autoregressive model for spatially correlated functional data

Conférences Internationales sans actes : CroNoS Workshop on Functional Data Analysis, Iasi, Roumanie,

Auteurs: T. Huang , G. Saporta , H. Wang , S. Wang

Mots clés: Functional linear model, spatial data, functional principal components

Résumé: The well-known functional linear regression model (FLM) has been developed under the assumption that the observations are independent. However, the independence assumption may often be violated in practice, especially when we collect data with network structure coming from various fields such as marketing, sociology or spatial economics. Yet relatively few works are available for FLM with network structure. We propose a novel spatial functional linear model (SFLM), incorporating a spatial autoregressive parameter and a spatial weight matrix in FLM to accommodate spatial dependence among individuals. The proposed model is flexible as it takes advantages of FLM in dealing with high dimensional covariates, and of spatial autoregressive model (SAR model) in capturing network dependence. We develop an estimation method based on functional principal components analysis (FPCA) and maximum likelihood estimation. The simulation studies show that our method performs as well as FPCA-based method for FLM when there is no network structure and outperforms the latter when there exists a network structure. A real dataset of weather data is also employed to demonstrate the utility of SFLM.

Commentaires: A satellite workshop of Compstat 2018, the 23rd International Conference on Computational Statistics

BibTeX

@conference {
	HSW18,
	title	=	"{SFLM: A mix of a Functional Linear Model and of a Spatial autoregressive model for spatially correlated functional data}",
	author	=	" T. Huang and G. Saporta and H. Wang and S. Wang ",
	year	=	2018,
	note	=	"{A satellite workshop of Compstat 2018, the 23rd International Conference on Computational Statistics}",
}