Median Regression
Median regression may refer to: * Quantile regression, a regression analysis used to estimate conditional quantiles such as the median * Repeated median regression In robust statistics, repeated median regression, also known as the repeated median estimator, is a robust linear regression algorithm. The estimator has a breakdown point of 50%. Although it is equivariant under scaling, or under linear transforma ...

Quantile Regression
Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares estimates the conditional ''mean'' of the response variable across values of the predictor variables, quantile regression estimates the conditional ''median'' (or other '' quantiles'') of the response variable. here is also a method for predicting the conditional geometric mean of the response variable, Tofallis (2015). "A Better Measure of Relative Prediction Accuracy for Model Selection and Model Estimation", ''Journal of the Operational Research Society'', 66(8):1352-1362/ref>.] Quantile regression is an extension of linear regression used when the conditions of linear regression are not met. Advantages and applications One advantage of quantile regression relative to ordinary least squares regression is that the quantile regression estimates are more robust against outliers in the response measurements. However, the main attraction of quantile reg ...
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