Title: Improved Quantile Regression Estimators when the Errors are Independently and Non-identically Distributed,
Abstract: In a classical regression model, it is usually assumed that the explanatory
variables are independent of each other and error terms are normally
distributed. But when these assumptions are not met, situations like the error
terms are not independent or they are not identically distributed or both of
these, LSE will not be robust. Hence, quantile regression has been used to
complement this deficiency of classical regression analysis and to improve the
least square estimation (LSE). In this study, we consider preliminary test and
shrinkage estimation strategies for quantile regression models with
independently and non-identically distributed (i.ni.d.) errors. A Monte Carlo
simulation study is conducted to assess the relative performance of the
estimators. Also, we numerically compare their performance with Ridge, Lasso,
Elastic Net penalty estimation strategies. A real data example is presented to
illustrate the usefulness of the suggested methods. Finally, we obtain the
asymptotic results of suggested estimators