Estimation and testing for a partially linear single-index spatial regression model

ABSTRACT

Observations recorded on ‘locations’ usually exhibit spatial dependence. In an effort to take into account both the spatial dependence and the possible underlying non-linear relationship, a partially linear single-index spatial regression model is proposed. This paper establishes the estimators of the unknowns. Moreover, it builds a generalized F-test to determine whether or not the data provide evidence on using linear settings in empirical studies. Their asymptotic properties are derived. Monte Carlo simulations indicate that the estimators and test statistic perform well. The analysis of Chinese house price data shows the existence of both spatial dependence and a non-linear relationship.

KEYWORDS:

• spatial dependence
• single index
• semiparametric generalized method of moments
• generalized F-test

• C12
• C13
• C14
• C21

ACKNOWLEDGEMENT

The authors thank the editor and referees for their valuable comments and suggestions.

DISCLOSURE STATEMENT

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 11271242]; and sponsored by both the Shuguang Program supported by the Shanghai Education Development Foundation and the Shanghai Municipal Education Commission [grant number 15SG31].