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A semiparametric spatial dynamic model. (English) Zbl 1297.62093

Starting from the Boston house price data, the authors set a semiparametric spatial dynamic model which extends both spatial autoregressive models and varying coefficient models by taking into account the effects of some covariates (crime rate, accessibility to highways and also, the location effects of the impacts of some covariates, the spatial neighboring effects). The estimation of the model is profile likelihood based. Another addressed issue is the number of unknown parameters related to bivariate function from the model which is solved based on the residual sum of squares of standard bivariate nonparametric regression model. Further using the AIC for the nonparametric version for the model selection, the authors identify which components from the model are constant and which are not. Two algorithms are proposed for the computation of AIC in order to find the smallest value, one based on the backward elimination and the other based on curvature to average ratio (faster but less accurate). The asymptotic properties of the model estimators are derived and both issues, estimation of the model and selection of the model are validated by a simulation study. An analysis of the proposed model is also done on real data of Boston house price. More precisely, using the proposed model and estimation/selection procedures, the authors study the effect of some factors (per capita crime rate by town, average number of room per dwelling, the accessibility to highways, full value property tax rate and the percentage of the lower status of the population) on the median value of the owner-occupied homes and location importance over the effects.

MSC:

62G08 Nonparametric regression and quantile regression
62G05 Nonparametric estimation
62G20 Asymptotic properties of nonparametric inference
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References:

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