GEOGRAPHICALLY WEIGHTED FUNCTIONAL MULTIPLE REGRESSION ANALYSIS: A NUMERICAL INVESTIGATION(Functional Data Analysis)

Functional regression analysis enables us to investigate the relationship among variables over time. Sometimes, however, we meet the case where regression coefficients do not remain fixed over space, when we analyze spatial data. The present paper proposes a method of geographically weighted functional regression analysis to analyze the relationship among variables which varies over space as well as over time, borrowing the idea of Brunsdon et al. (1998) in which geographical weight is considered in ordinary regression. Monte Carlo and bootstrap methods are used to perform the statistical test for spatial variability and to evaluate the reliability of the prediction. The proposed methods are illustrated using a real data set.