Title: Pretest and Stein-Type Estimations in Quantile Regression Model,
Abstract: In this study, we consider preliminary test and shrinkage estimation
strategies for quantile regression models. In classical Least Squares
Estimation (LSE) method, the relationship between the explanatory and explained
variables in the coordinate plane is estimated with a mean regression line. In
order to use LSE, there are three main assumptions on the error terms showing
white noise process of the regression model, also known as Gauss-Markov
Assumptions, must be met: (1) The error terms have zero mean, (2) The variance
of the error terms is constant and (3) The covariance between the errors is
zero i.e., there is no autocorrelation. However, data in many areas, including
econometrics, survival analysis and ecology, etc. does not provide these
assumptions. First introduced by Koenker, quantile regression has been used to
complement this deficiency of classical regression analysis and to improve the
least square estimation. The aim of this study is to improve the performance of
quantile regression estimators by using pre-test and shrinkage strategies. A
Monte Carlo simulation study including a comparison with quantile $L_1$--type
estimators such as Lasso, Ridge and Elastic Net are designed to evaluate the
performances of the estimators. Two real data examples are given for
illustrative purposes. Finally, we obtain the asymptotic results of suggested
estimators