An important issue is that the respiratory mortality may be a result of airpollution 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 theordinary least squares regression, which has some assumptions, also known asGauss-Markov assumptions, on the error term showing white noise process of theregression model. However, in many applications, especially for this example,these assumptions are not satisfied. Therefore, in this study, a quantileregression approach is used to model the respiratory mortality using thementioned explanatory variables. Moreover, improved estimation techniques suchas preliminary testing and shrinkage strategies are also obtained when theerrors are autoregressive. A Monte Carlo simulation experiment, including thequantile penalty estimators such as Lasso, Ridge and Elastic Net, is designedto evaluate the performances of the proposed techniques. Finally, thetheoretical risks of the listed estimators are given.
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