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Estimation of nonparametric additive models with high order spatial autoregressive errors
Author(s) -
Xu Guoying,
Bai Yang
Publication year - 2021
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11565
Subject(s) - estimator , nonparametric statistics , autoregressive model , asymptotic distribution , mathematics , additive model , nonparametric regression , asymptotic analysis , consistency (knowledge bases) , moment (physics) , econometrics , statistics , physics , classical mechanics , geometry
In this article, we propose nonparametric generalized method of moments estimation for nonparametric additive models with high order spatial autoregressive dependence. The estimation procedure is derived in three steps by combining a spline‐backfitting method with generalized moment conditions that relieve correlations within the dependent variables. Consistency and asymptotic normality are demonstrated under mild conditions. Specifically, compared with estimators of nonparametric functions that ignore cross‐sectional dependence in errors, the resultant estimators that consider the error term are asymptotically more efficient and achieve the well‐known oracle properties. Simulation studies investigating the finite sample performance of the estimation procedure confirm the validity of our asymptotic theory. An application to the Boston housing data serves as a practical illustration.