Kvantilregression

Kvantilregression, also known as quantile regression, is a statistical technique used to estimate the conditional quantiles of a response variable given certain predictor variables. Unlike traditional linear regression, which estimates the conditional mean, quantile regression provides a more comprehensive view of the relationship between variables by modeling the entire conditional distribution of the response variable.

The method was introduced by Roger Koenker and Gilbert Bassett in 1978. It is particularly useful in situations where the relationship between the response and predictor variables is not linear or where the data contains outliers or heteroscedasticity. Quantile regression can be applied to various types of data, including continuous, discrete, and censored data.

The key advantage of quantile regression is its ability to provide robust estimates of the conditional quantiles, which can be used to construct prediction intervals, assess the impact of predictors on different parts of the response distribution, and detect changes in the relationship between variables over time. It is widely used in fields such as economics, finance, environmental science, and social sciences.

Quantile regression can be performed using various software packages, including R, Python, and SAS. The most common approach is to use linear programming or optimization techniques to minimize the sum of absolute deviations between the observed and predicted quantiles. The resulting estimates are less sensitive to outliers and can provide more accurate and reliable predictions than traditional linear regression.