Quantile regression is a type of regression analysis used in statistics that estimates the relationship between independent variables and specific quantiles (percentiles) of the dependent variable's distribution, rather than just focusing on the mean (as in ordinary least squares regression). This method allows for a more comprehensive analysis of the impact of independent variables across different points in the distribution of the dependent variable.
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Quantile regression models a conditional quantile of a response, rather than its conditional mean. Fitting by the check loss uses an asymmetric absolute-error penalty, so different values of describe different parts of the response distribution. Nonlinear models may use any identifiable continuous regression function, not only a linear predictor.