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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.
The intercept and slope of a linear regression between the quantiles gives a measure of the relative location and relative scale of the samples. If the median of the distribution plotted on the horizontal axis is 0, the intercept of a regression line is a measure of location, and the slope is a measure of scale.
Less common forms of regression use slightly different procedures to estimate alternative location parameters (e.g., quantile regression or Necessary Condition Analysis [1]) or estimate the conditional expectation across a broader collection of non-linear models (e.g., nonparametric regression).
The well-known ordinary least squares (OLS) averaging [10] uses linear regression to estimate weights of the point forecasts of individual models. Replacing the quadratic loss function with the absolute loss function leads to quantile regression for the median, or in other words, least absolute deviation (LAD) regression. [11]
Given a sample from a normal distribution, whose parameters are unknown, it is possible to give prediction intervals in the frequentist sense, i.e., an interval [a, b] based on statistics of the sample such that on repeated experiments, X n+1 falls in the interval the desired percentage of the time; one may call these "predictive confidence intervals".
Median regression may refer to: Quantile regression , a regression analysis used to estimate conditional quantiles such as the median Repeated median regression , an algorithm for robust linear regression
There is one fewer quantile than the number of groups created. Common quantiles have special names, such as quartiles (four groups), deciles (ten groups), and percentiles (100 groups). The groups created are termed halves, thirds, quarters, etc., though sometimes the terms for the quantile are used for the groups created, rather than for the ...
Linear quantile regression models a particular conditional quantile, for example the conditional median, as a linear function β T x of the predictors. Mixed models are widely used to analyze linear regression relationships involving dependent data when the dependencies have a known structure. Common applications of mixed models include ...