Imputed quantile tensor regression for near-sited spatial-temporal data

Abstract

Modern spatial temporal data are collected from sensor networks. Missing data problems are common for this kind of data. Making robust and accurate imputation is important in many applications. There are complex correlations in both spatial and temporal dimensions. Thus, it is even a challenge to model missing spatial-temporal data. In this article, the imputation of missing values is with the help of related covariates. First, we transform the original sensor × time observational matrix to a high order tensor by adding an extra temporal dimension. Then we integrate quantile tensor regression with tensor completion. The objective function includes check loss and nuclear norm penalty. An alternating update algorithm combined with alternating direction method of multipliers (ADMM) is developed to solve the objective function. Theoretical properties of the proposed estimator are investigated. Simulation studies show our proposed method is more robust and can get more accurate imputation results. Real data analysis about Beijing's PM2.5 concentration level is conducted to verify the efficiency of the estimation procedure.