Estimation Of Spatio-Temporal Kernel Variable Coefficient Regression Model And Its Application

In recent years,the availability and accessibility of spatio-temporal data have been greatly enhanced.Especially with the advent of the era of big data,spatiotemporal analysis and modeling have been widely concerned.Many researches are carried out in this field.The development of geographical and temporal weighted regression model provides a powerful tool for dealing with spatiotemporal nonstationarity of the regression relationship.But the method often assumes that the temporal covariates are continuous data,and cannot separate temporal and spatial effects to directly obtain the temporal and spatial bandwidth parameters.In addition,the temporal and spatial analysis of epidemiology have attracted increasing attention.Hand,foot and mouth disease(HFMD)is a common acute infectious disease.The epidemic of the disease has seriously endangered children's health and public health security.However,there are relatively few studies on the heterogeneity of HFMD at the spatio-temporal level.Especially,there are little study about characteristics of temporal and spatial influence factors of HFMD in Xinjiang.For spatio-temporal data with discrete time variables,this thesis introduces a spatiotemporal kernel variation coefficient regression model to simultaneously optimise different bandwidth parameters.The model is further applied in the analysis of spatio-temporal HFMD data in Xinjiang to explore the spatio-temporal variation characteristics of the influence of various factors on the incidence.First,this thesis constructs a spatio-temporal kernel variable coefficient regression model.Based on the continuous kernel in space and discrete kernel in time,a mixed spatio-temporal kernel function is constructed to generate the spatio-temporal weight matrix.And the coefficient functions in the model are estimated by a locally weighted least squares method.In simulations,mean square error,Akaike information criterion,the square of deviance and estimated surfaces of the coefficient functions are compared.Simulation results show the estimation results of the spatio-temporal kernel variable coefficient regression model has high accuracy,validity,and satisfactory performance in exploring the underlying spatio-temporal patterns of the data.Secondly,to test the spatio-temporal non-stationarity of the regression relationship of the model,two test statistics are constructed according to the generalized likelihood ratio theory.-values of tests are obtained through Bootstrap method based on residuals.Through simulation experiments,it is proved that the test has strong power.This thesis investigates the spatial and temporal variation of HFMD incidence in 101 cities and counties in Xinjiang from January to December 2018 under the spatio-temporal kernel variation coefficient regression model.We explores the characteristics of five meteorological factors,namely monthly average temperature,average rainfall,average pressure,average wind speed and relative humidity,on the incidence of HFMD in Xinjiang.In addition,descriptive statistical analyses and spatial autocorrelation analyses are conducted to discuss the epidemiological characteristics and spatial clustering patterns of HFMD in Xinjiang.The study found that: 1)In 2018,patients of HFMD in Xinjiang were mainly children in nursery and scattered.The incidences among different age groups were extremely unbalanced,with children between 0 and 5 years old as the main susceptible population.Incidence of HFMD in summer season was the highest,with two peak of incidence in June and October.2)The high-high clustering areas of HFMD were mainly Urumqi City and its nearby areas in northern Xinjiang.3)The influence of meteorological factors on the incidence of HFMD had seasonal characteristics.The intensity and direction of influence had obvious temporal and spatial heterogeneity at different times and counties.The monthly average rainfall had a relatively weak effect on HFMD.Moderate air pressure and wind speed accelerated the spread of HFMD.But excessive wind speed or high air pressure had an opposite effect on its prevalence.