Abstract
There has been a growing interest on using nonparametric and semiparametric modelling techniques for the analysis of spatial data because of their powerfulness in extracting the underlying local patterns in the data. In this study, stimulated by the Boston house price data, we apply a semiparametric spatial additive model to incorporation of spatial e ects in regression models. For this semiparametric model, we develop a linear hypothesis test of parametric coecients as well as a test for the existence of the spatial e ects. For the problem of variable selection, the adaptive Lasso method was applied. Monte Carlo simulation studies are conducted to illustrate the finite sample performance of the proposed inference procedures. Finally, an application in Boston housing data is studied.
Highlights
The Boston house price data of Rubinfeld (1978) and Gilley and Pace (1996) is frequently used in literature to illustrate some new statistical methods
For comparison with the adaptive Lasso (ALASSO), we evaluate the mean squared error (MSE) of the least absolute shrinkage and selection operator (LASSO), ORACLE and FULL model estimators
Thirteen explanatory variables include levels of nitrogen oxides (NOX), average number of rooms (RM), proportion of structures built before 1940 (AGE), black population proportion (B), lower status population proportion (LSTAT), crime rate (CRIM), proportion of area zoned with large lots (ZN), proportion of nonretail business areas (INDUS), property tax rate (TAX), pupilteacher ratio (PTRATIO), location contiguous to the Charles River (CHAS), weighted distances to the employment centers (DIS), and an index of accessibility (RAD)
Summary
The Boston house price data of Rubinfeld (1978) and Gilley and Pace (1996) is frequently used in literature to illustrate some new statistical methods. For the Boston house price data, to capture the “large-scale” locational effects between response variable and the associated 13 covariates, Pace and Gilley (1997) proposed the following linear regression model yi = β j xi j + β14uivi + β15ui + β16vi + β17u2i + β18v2i + εi, i = 1, 2, · · · , 506,. Sometimes, the quadratic expression involving latitude and longitude is not adequate for the real locational effects. To solve this problem, we apply the following semiparametric spatial additive model to fit the data set yi = f (ui) + g(vi) + xTi β + εi, i = 1, 2, · · · , n,.
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