Jump Detection Of Two-dimensional Threshold In Spatial Linear Regression Model

This paper aims at spatial climate statistics,focusing on two districts of Shaanxi Province:Shaannan district and Guanzhong district.There is a boundary line between Shaannan district and Guanzhong district called the Qinling-Huaihe line.It is easily found that there are obvious climate differences on both sides of the Qinling-Huaihe.Because there is a linear relationship between the spatial climate data and the agricultural output data,the spatial linear regression model can be used to detect the location curve of two adjacent areas,namely the threshold curve.Based on the classical spatial linear regressions,we use two position variables including longitude and latitude as threshold variables instead of the independent variables in classical problems.The threshold curve divides the sample data into two parts,and they separately satisfy the spatial linear model with different regression coefficients.In order to simplify,here the threshold curve is regarded as a straight line which can be expressed by the position variables and can be estimated by maximizing the differences between regression coefficients on both sides.In order to test whether there are differences between the two groups of sample data,the issue will be considered by hypothesis testing,and get the limit distribution of statistics when the null hypothesis and the alternative hypothesis hold respectively.For the estimation problem of 2-dimensional threshold in the spacial linear regression model,the estimation method of threshold parameters is proposed,and series of asymptotic properties of these estimators are studied.Finally,the Monte Carlo simulation and an empirical simulation are used to verify the rationality of the model and the effectiveness of the selected parameter estimation procedure.