Positively constrained quantile regression {consrq} | R Documentation |
Positively constrained quantile regression
Description
Positively constrained quantile regression.
Usage
prq(y, x, tau = 0.5)
mprq(y, x, tau = 0.5)
Arguments
y |
The response variable. For the prq() a numerical vector with observations, but for the mprq() 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 (including the constant) are non negative. That is,
min \sum_{i=1}^n|y_i-\bm{x}_i^\top\bm{\beta}|
such that \beta_j \geq 0
.
The pls() function performs a single regression model, whereas the mpls() 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(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)
prq(y, x)