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Quantile Regression
Roger Koenker, in International Encyclopedia of the Social & Behavioral Sciences (Second Edition), 2015
Quantile regression is a statistical technique intended to estimate, and conduct inference about, conditional quantile functions. Just as classical, linear regression methods based on minimizing sums of squared residuals enable one to estimate models for conditional mean functions, quantile regression methods offer a mechanism for estimating models for the conditional median function, and the full range of other conditional quantile functions. By supplementing the estimation of conditional mean functions with techniques for estimating an entire family of conditional quantile functions, quantile regression is capable of providing a more complete statistical analysis of the stochastic relationships among random variables.
Quantile regression makes no assumptions about the distribution of the residuals. It also lets you explore different aspects of the relationship between the dependent variable and the independent variables. There are at least two motivations for quantile regression: Suppose our dependent variable is bimodal or multimodal that is, it.