Estimation of partially linear single-index spatial autoregressive model

  • Suli Cheng
  • Jianbao ChenEmail author
Regular Article


In this paper, we first present partially linear single-index spatial autoregressive model and propose its profile maximum likelihood estimators (PMLE). Subsequently, consistency and asymptotic normality of the estimators for parameters and unknown link function are derived under some regular conditions. Thirdly, Monte Carlo simulations are used to investigate the performances of these estimators in finite sample cases. Finally, the proposed method is illustrated with the real data set of Boston Housing Price.


Partially linear single-index spatial autoregressive model Profile maximum likelihood estimation Consistency Asymptotic normality Monte Carlo simulation 



The authors thanks the editors Christine H. Müller and Jessica Jeske for the valuable suggestions. We are also grateful to referees for careful reading of the manuscript and comments with lead to an improved version of the paper. This work is supported by National Social Sciences Foundation of China (16BTJ018), National Natural Science Foundation of China (71503220), Key Research Base for Humanities and Social Sciences of Ministry of Education (15JJD790029), Humanities and Social Sciences of Ministry of Education of China (13YJA9100002), Natural Science Foundation of Fujian Province (2017J01396, 2018J05002), Program for Innovative Research Team in Science and Technology in Fujian Province University, Fujian Normal University Innovation Team Foundation “Probability and Statistics: Theory and Application” (IRTL1704).


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Mathematics and InformaticsFujian Normal UniversityFuzhouPeople’s Republic of China

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