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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 Theil–Sen estimator is a simple robust estimation technique that chooses the slope of the fit line to be the median of the slopes of the lines through pairs of sample points. It has similar statistical efficiency properties to simple linear regression but is much less sensitive to outliers .
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%. [ 1 ] Although it is equivariant under scaling, or under linear transformations of either its explanatory variable or its response variable, it is not under affine ...
The general form of its probability density function is [2] [3] = (). The parameter μ {\textstyle \mu } is the mean or expectation of the distribution (and also its median and mode ), while the parameter σ 2 {\textstyle \sigma ^{2}} is the variance .
L-estimators can also be used as statistics in their own right – for example, the median is a measure of location, and the IQR is a measure of dispersion. In these cases, the sample statistics can act as estimators of their own expected value; for example, the sample median is an estimator of the population median.
In statistics, the Hodges–Lehmann estimator is a robust and nonparametric estimator of a population's location parameter.For populations that are symmetric about one median, such as the Gaussian or normal distribution or the Student t-distribution, the Hodges–Lehmann estimator is a consistent and median-unbiased estimate of the population median.
Such an estimator is not necessarily an M-estimator of ρ-type, but if ρ has a continuous first derivative with respect to , then a necessary condition for an M-estimator of ψ-type to be an M-estimator of ρ-type is (,) = (,). The previous definitions can easily be extended to finite samples.
The term "variance structure" refers to the algebraic form of the covariance matrix between outcomes, Y, in the sample. Examples of variance structure specifications include independence, exchangeable, autoregressive, stationary m-dependent, and unstructured.