Spatial Autoregressive Mode Parameter Estimation and Inference Using Stochastic Gradient Descent and Bootstrap Perturbation

• Activity Number: 288 - SLDS CSpeed 5
• Type: Contributed
• Date/Time: Wednesday, August 11, 2021 : 1:30 PM to 3:20 PM
• Sponsor: Section on Statistical Learning and Data Science
• Author(s): Ji Meng Loh* and Gan Luan
• Companies: New Jersey Institute of Technology and New Jersey Institute of Technology
• Keywords: Spatial autoregressive models; stochastic gradient descent; bootstrap perturbation

Abstract

A perturbation method for the stochastic gradient descent procedure was introduced recently by Fang et al (2018) for independent data which allows parameter estimation and inference to occur through one pass of the data, making it suitable for large-scale data or data streams. We study its use for spatial data, in particular, for parameter estimation and inference for the spatial autoregressive model. Through simulation studies we find that the empirical coverage of confidence intervals for the variance and regression parameters match the nominal levels, but not so for the correlation parameter. We examine various ways to modify the perturbation method to improve the empirical coverage.