Quantile Regression

In the field of regression, the presence of outliers can cause inefficiency in estimation of the least squares method. This presence enables to use robust regression method which is based on the relationship between two variables x and,y. Methodology does not allow to be affected by violations of assumptions in the generation process underlying data. Within these methods, one is the object of this research:quantile regression is a statistical method used by scientists to study the relationship between the variables. In this thesis, I will consider the same type of relationship to explain the history and the use of the quantile regression starting with quantiles, linear regression and specifying properties and application examples, established methods complement regression from methods (least squares). I will compare it with ordinary least square coefficients and some robust regressions at the end I will give an important application in some areas.(Such as econometric, ecology, etc....).