Regression quantiles

Title: Regression Quantiles Author: Peter Rusnák Department: Department of Probabilty and Mathematical Statistics Supervisor: RNDr. Jan Kalina, Ph.D.,Institute of Computer Science, AS CR Abstract: Quantile regression is a statistical method for specifying dependencies among variables, which was introduced by Koenker a Bassett in 1978. Since that time it has gone through a big development, when its theoretical properties have been under study, and it also has found many practical applications for data processing in variety of fields.While ordinary least-squares regression describes the relationship between one or more covariates X and the conditional mean of a response variable Y given X = x, quantile regression describes the relationship between X and the conditional quantiles of variable Y given X = x. This work contains the theory necessary for understanding relationship between standard and quantile regression and enabling include so received estimates to bigger group of M-estimates. The computation of coefficients for particular covariates is made by using Frisch-Newton algorithm belonging to methods of linear programming. The so-called regression ranks are also obtained as a by-product of this algorithm and we discuss their computational aspects and usage for hypothesis testing.In the second part, we..