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Title: Permutation tests for testing hypotheses in spatial regression model with functional response Authors:  Eva Fiserova - Palacky University (Czech Republic) [presenting]
Veronika Rimalova - Palacky University Olomouc (Czech Republic)
Alessandra Menafoglio - Politecnico di Milano (Italy)
Alessia Pini - Universita Cattolica del Sacro Cuore (Italy)
Abstract: The aim is to introduce an approach to hypothesis testing in a functional linear model for spatial data. The proposed method can deal with the spatial structure of data by building a permutation testing procedure on spatially filtered residuals of a spatial regression model. Indeed, due to the spatial dependence existing among the data, the residuals of the regression model are not exchangeable, breaking the basic assumptions of the Freedman and Lane permutation scheme. Instead, it is proposed here to base the permutation test on approximately exchangeable spatially filtered residuals. To evaluate the performance of the proposed method in terms of empirical size and power, a simulation study, examining its behaviour under different covariance settings, is conducted. It will be shown that neglecting the residuals' spatial structure in the permutation scheme (thus permuting the correlated residuals directly) yields a very liberal testing procedure, whereas the proposed procedure based on spatially filtered residuals is close to the nominal size of the test. The methodology will be demonstrated on a real-world data set on the amount of waste production in the Venice province of Italy.