DATA ANALYSIS USING REGRESSION MODELS WITH TIME DEPENDENT AND EXTREME ERRORS: APPLICABLE TO AIR POLLUTION DATA

This paper develops a statistical methodology to handle regression of time series data (auto-regressive) with extreme errors. Since in most environmental sciences studies data are gathered in periodic times, this type of data appears more often. An estimation strategy is developed based on regression quantiles to deal with this problem. This is an extension of the Trimmed Least Squares Estimators (TLSE) method to a regression model with auto-regression errors, namely, mixed model. It generalizes the TLSE of regression models to the TLSE of mixed model parameters based on randomly weighted empirical process. It uses regression and auto-regression quantiles. Finally, we apply the results to some air pollution data gathered in Isfahan.