Improving estimations in quantile regression model with autoregressive errors

Abstract

An important issue is that the respiratory mortality may be a result of air pollution which can be measured by the following variables: temperature, relative humidity, carbon monoxide, sulfur dioxide, nitrogen dioxide, hydrocarbons, ozone and particulates. The usual way is to fit a model using the ordinary least squares regression, which has some assumptions, also known as Gauss-Markov assumptions, on the error term showing white noise process of the regression model. However, in many applications, especially for this example, these assumptions are not satisfied. Therefore, in this study, a quantile regression approach is used to model the respiratory mortality using the mentioned explanatory variables. Moreover, improved estimation techniques such as preliminary testing and shrinkage strategies are also obtained when the errors are autoregressive. A Monte Carlo simulation experiment, including the quantile penalty estimators such as Lasso, Ridge and Elastic Net, is designed to evaluate the performances of the proposed techniques. Finally, the theoretical risks of the listed estimators are given.

On the Preliminary Test Generalized Liu Estimator with Series of Stochastic Restrictions

“…Afterward, researchers endeavored to develop preliminary test estimators in different fields of statistical inference. Among others, we refer to the studies by Saleh and Sen (1978), Saleh (2006), Roozbeh (2015) and references therein, and more recently Yuzbasi et al (2017), Wu and Asar (2017), and Yuzbasi et al (2018).…”