Quantile Regression for Partially Linear Varying Coefficient Spatial Autoregressive Models

TL;DR

This paper develops a quantile regression method for partially linear spatial autoregressive models with varying coefficients, employing B-splines and instrumental variables, and establishes their theoretical properties.

Contribution

It introduces a novel quantile regression approach with B-spline approximation and instrumental variables for spatial models, including hypothesis testing procedures.

Findings

Method performs well in finite samples based on simulations.

Theoretical properties of estimators and tests are rigorously established.

Real data analysis demonstrates practical applicability.

Abstract

This paper considers the quantile regression approach for partially linear spatial autoregressive models with possibly varying coefficients. B-spline is employed for the approximation of varying coefficients. The instrumental variable quantile regression approach is employed for parameter estimation. The rank score tests are developed for hypotheses on the coefficients, including the hypotheses on the non-varying coefficients and the constancy of the varying coefficients. The asymptotic properties of the proposed estimators and test statistics are both established. Monte Carlo simulations are conducted to study the finite sample performance of the proposed method. Analysis of a real data example is presented for illustration.