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