Positive and unit sum constrained quantile regression {consrq}R Documentation

Positive and unit sum constrained quantile regression

Description

Positive and unit sum constrained quantile regression.

Usage

pcrq(y, x, tau = 0.5)
mpcrq(y, x, tau = 0.5)

Arguments

y

The response variable. For the pcrq() a numerical vector with observations, but for the mpcrq() a numerical matrix.

x

A matrix with independent variables, the design matrix.

tau

The quantile(s) to be estimated, a number strictly between 0 and 1. It a vector of values between 0 and 1; in this case an object of class "rqs" is returned containing among other things a matrix of coefficient estimates at the specified quantiles.

Details

The constraint is that all beta coefficients are positive and sum to 1. That is, i.e. min \sum_{i=1}^n(y_i-\bm{x}_i^\top\bm{\beta})^2 such that \beta_j \geq 0 and \sum_{j=1}^d\beta_j=1. The pcrq() function performs a single regression model, whereas the mpcrq() function performs a regression for each column of y. Each regression is independent of the others.

Value

A list including:

be

A numerical matrix with the positively constrained beta coefficients.

mae

A numerical vector with the mean absolute error.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris mtsagris@uoc.gr.

See Also

prq

Examples

x <- as.matrix( iris[1:50, 1:4] )
y <- rnorm(50)
pcrq(y, x)

[Package consrq version 1.0 Index]