Layman’s abstract for paper on estimation of nonparametric additive models with high order spatial autoregressive errors

Each week, we will be publishing layman’s abstracts of new articles from our prestigious portfolio of journals in statistics. The aim is to highlight the latest research to a broader audience in an accessible format.

The article featured today is from the Canadian Journal of Statistics, with the full article now available to read in Early View here.

Xu, G. and Bai, Y. (2020), Estimation of nonparametric additive models with high order spatial autoregressive errors. Can J Statistics. doi:10.1002/cjs.11565

Often because of the complexity of sociological quantitative analysis, the data involved are difficult to fit with simple linear models, and non-parametric additive models become a common model because of fewer model assumptions. In addition, sociological studies often have to consider the spatial dependence of the data, as inter-regional mobility and differences also contribute to the bias of the model analysis. Combining the robustness of non-parametric models with the excellent nature of spatial autoregression, this paper proposes a non-parametric additive model with a high-order spatial autoregression error and gives relatively valid estimates of the unknown parameter and non-parametric parts of the model. The estimation procedure is derived in three steps by combining spline-backfitted method with generalized moment conditions which relieving correlations within the dependent variables. Specifically, compared with the estimators of nonparametric functions which ignores the cross sectional dependence in errors, the resultant estimators considering the error term is asymptotically more efficient and achieve the well known oracle properties. Numerous Monte Carlo simulations and analysis of Boston house price data demonstrate the limited sample performance of our proposed model and estimation methods. We believe that the proposed approach can provide sociological researchers with a flexible and robust modeling tool.