| Type: | Package |
| Title: | Constrained Quantile Regression |
| Version: | 1.0 |
| Date: | 2024-11-20 |
| Author: | Michail Tsagris [aut, cre] |
| Maintainer: | Michail Tsagris <mtsagris@uoc.gr> |
| Depends: | R (≥ 4.0) |
| Suggests: | Rfast2, cols |
| Imports: | quantreg, Rfast |
| Description: | Constrained quantile regression is performed. One constraint is that all beta coefficients (including the constant) cannot be negative, they can be either 0 or strictly positive. Another constraint is that the beta coefficients lie within an interval. References: Koenker R. (2005) Quantile Regression, Cambridge University Press. <doi:10.1017/CBO9780511754098>. |
| License: | GPL-2 | GPL-3 [expanded from: GPL (≥ 2)] |
| NeedsCompilation: | no |
| Packaged: | 2024-11-20 13:44:36 UTC; mtsag |
| Repository: | CRAN |
| Date/Publication: | 2024-11-21 08:00:03 UTC |
Constrained Quantile Regression
Description
Constrained quantile regression is performed. One constraint is that all beta coefficients (including the constant) cannot be negative. They can be either 0 or strictly positive. Another constraint is that the beta coefficients lie within an interval.
Details
| Package: | consrq |
| Type: | Package |
| Version: | 1.0 |
| Date: | 2024-11-20 |
Maintainers
Michail Tsagris <mtsagris@uoc.gr>.
Author(s)
Michail Tsagris mtsagris@uoc.gr
References
Koenker R. (2005) Quantile Regression, Cambridge University Press.
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)
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
Examples
x <- as.matrix( iris[1:50, 1:4] )
y <- rnorm(50)
pcrq(y, x)
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)