Lower and upper bound constrained quantile regression {consrq}R Documentation

Lower and upper bound constrained quantile regression

Description

Lower and upper bound constrained quantile regression.

Usage

int.crq(y, x, tau = 0.5, lb, ub)
int.mcrq(y, x, tau = 0.5, lb, ub)

Arguments

y

For the int.crq() the response variable, a numerical vector with observations, but a matrix of response variables for the int.mcrq().

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.

lb

A vector or a single value with the lower bound(s) in the coefficients.

ub

A vector or a single value with the upper bound(s) in the coefficients.

Details

This function performs quantile regression under the constraint that the beta coefficients lie within interval(s), i.e. min \sum_{i=1}^n|y_i-\bm{x}_i^\top\bm{\beta}| such that lb_j\leq \beta_j \leq ub_j.

Value

A list including:

be

A numerical matrix with the constrained beta coefficients.

mae

A numerical vector with the mean absolute error(s).

Author(s)

Michail Tsagris.

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

See Also

prq, pcrq

Examples

x <- as.matrix( iris[1:50, 1:4] )
y <- rnorm(50)
int.crq(y, x, lb = -0.2, ub = 0.2)

[Package consrq version 1.0 Index]