Recent progress of nonlinear spatial modelling with nonparametric and semiparametric approaches: A personal review

Prof Zudi Lu (University of Southampton)

Frank Adams 2,

Larger amounts of spatial or spatiotemporal data with more complex structures collected at irregularly spaced sampling locations are prevalent in a wide range of disciplines. With few exceptions, however, practical statistical methods for nonlinear modeling and analysis of such data remain elusive. In this talk, I provide a review on some developments and progress of the research that my co-authors and I have recently done. In particular, we will look at some nonparametric methods for probability, including joint, density estimation, and semiparametric models for a class of spatio-temporal autoregressive partially nonlinear regression models permitting possibly nonlinear relationships between responses and covariates. In the setting of semiparametric spatiotemporal modelling, I will also show a computationally feasible data-driven method for spatial weight matrix estimation. For illustration, our methodology is applied to investigate some land and housing prices data sets. 

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