Search

This study developed a new method of hypothesis testing of model conformity between truncated spline nonparametric regression influenced by spatial heterogeneity and truncated spline nonparametric regression. This hypothesis test aims to determine the most appropriate model used in the analysis of spatial data. The test statistic for model conformity hypothesis testing was constructed based on the likelihood ratio of the parameter set under H0 whose components consisted of parameters that were not influenced by the geographical factor and the set under the population parameter whose components consisted of parameters influenced by the geographical factor. We have proven the distribution of test statistics V and verified that each of the numerators and denominators in the statistic test V followed a distribution of χ2. Since there was a symmetric and idempotent matrix S, it could be proved that Y~TS  Y~/σ2~χn-lm-12. Matrix Dui,vi was positive semidefinite and contained weighting matrix Wui,vi which had different values in every location; therefore matrix Dui,vi was not idempotent. If Y~TDui,viY~≥0 and Dui,vi was not idempotent and also Y~ was a N0,I distributed random vector, then there were constants k and r; hence Y~TDui,viY~~kχr2; therefore it was concluded that test statistic V followed an F distribution. The modeling is implemented to find factors that influence the unemployment rate in 38 areas in Java in Indonesia. [ABSTRACT FROM AUTHOR]

Nonparametric geographically weighted regression with truncated spline approach is a new method of statistical science. It is used to solve the problems of regression analysis of spatial data if the regression curve is unknown. This method is the development of nonparametric regression with truncated spline function approach to the analysis of spatial data. Spline truncated approach can be a solution for solving the modeling problem of spatial data analysis if the data pattern between the response and the predictor variables is unknown or regression curve is not known. This study focused on finding the estimators of the model nonparametric geographically weighted regression by maximum likelihood estimator (MLE) and then these estimators are investigated the unbiased property. The results showed nonparametric geographically weighted regression with truncated spline approach can be used in spatial data to solve problems regression curve that cannot be identified. [ABSTRACT FROM AUTHOR]