分位数回归估计结果方法

RT：有偿求解答

Quantile regression is a type of regression analysis used in statistics and econometrics. Whereas the method of least squares results in estimates that approximate the conditional mean of the response variable given certain values of the predictor variables, quantile regression aims at estimating either the conditional median or other quantiles of the response variable.

Advantages and applications
Quantile regression is desired if conditional quantile functions are of interest. One advantage of quantile regression, relative to the 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 regression goes beyond that. In practice we often prefer using different measures of central tendency and statistical dispersion to obtain a more comprehensive analysis of the relationship between variables.

In ecology, quantile regression has been proposed and used as a way to discover more useful predictive relationships between variables in cases where there is no relationship or only a weak relationship between the means of such variables. The need for and success of quantile regression in ecology has been attributed to the complexity of interactions between different factors leading to data with unequal variation of one variable for different ranges of another variable.

Another application of quantile regression is in the areas of growth charts, where percentile curves are commonly used to screen for abnormal growth; see Wei et al. (2005) and Wei and He (2006).

[edit] Mathematics
The mathematical forms arising from quantile regression are distinct from those arising in the method of least squares. The method of least squares leads to a consideration of problems in an inner product space, involving projection onto subspaces, and thus the problem of minimizing the squared errors can be reduced to a problem in numerical linear algebra. Quantile regression does not have this structure, and instead leads to problems in linear programming that can be solved by the simplex method. The fact that the algorithms of linear programming appear more esoteric to some users may explain partially why quantile regression has not been as widely used as the method of least squares.

check http://en.wikipedia.org/wiki/Quantile_regression

学习中