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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 median trick is a generic approach that increases the chances of a probabilistic algorithm to succeed. [1] Apparently first used in 1986 [ 2 ] by Jerrum et al. [ 3 ] for approximate counting algorithms , the technique was later applied to a broad selection of classification and regression problems.
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 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 statistics, a generalized estimating equation (GEE) is used to estimate the parameters of a generalized linear model with a possible unmeasured correlation between observations from different timepoints. [1] [2]
One can compute this directly, without using a probability distribution (distribution-free classifier); one can estimate the probability of a label given an observation, (| =) (discriminative model), and base classification on that; or one can estimate the joint distribution (,) (generative model), from that compute the conditional probability ...
The conditional variance tells us how much variance is left if we use to "predict" Y. Here, as usual, E ( Y ∣ X ) {\displaystyle \operatorname {E} (Y\mid X)} stands for the conditional expectation of Y given X , which we may recall, is a random variable itself (a function of X , determined up to probability one).
In statistics, the method of moments is a method of estimation of population parameters.The same principle is used to derive higher moments like skewness and kurtosis. It starts by expressing the population moments (i.e., the expected values of powers of the random variable under consideration) as functions of the parameters of interest.
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