Abstract
This article presents a partially linear additive spatial error model (PLASEM) specification and its corresponding generalized method of moments (GMM). It also derives consistency and asymptotic normality of estimators for the case with a single nonparametric term and an arbitrary number of nonparametric additive terms under some regular conditions. In addition, the finite sample performance for our estimates is assessed by Monte Carlo simulations. Lastly, the proposed method is illustrated by analyzing Boston housing data.
Highlights
We study the asymptotic properties of estimators for an arbitrary number of nonparametric additive terms
We present a partially linear additive spatial error model
This model can effectively avoid the “curse of dimensionality” in the nonparametric spatial autoregressive model and enhance the robustness of estimation, but it investigates the spatial autocorrelation of error terms, and captures the linearity and nonlinearity between the response variable and the interesting regressors simultaneously
Summary
Li and Mei [10] studied statistical inference of a profile quasi-maximum likelihood estimator based on the partially linear spatial autoregressive model in Su and Jin [14]. These models face the problem of “curse of dimensionality”, namely, their nonparametric estimation precision decreases rapidly as the dimension of explanatory variables increases. Dai et al [19] considered a quantile regression approach for partially linear varying coefficients in the SAR model and established asymptotic properties of estimators and test statistics. Du et al [20] presented a partially linear additive SAR model, constructed GMM estimation of the model, and proved the asymptotic properties of estimators.
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