Constrained least squares {cols}

Constrained least squares

Description

Constrained least squares.

Usage

cls(y, x, R, ca)

Arguments

y

The response variables, a numerical vector with observations.

x

A matrix with independent variables, the design matrix.

R

The R vector that contains the values that will multiply the beta coefficients. See details and examples.

ca

The value of the constraint, R^T \beta = c. See details and examples.

Details

This is described in Chapter 8.2 of Hansen (2019). The idea is to inimise the sum of squares of the residuals under the constraint R^T \beta = c. As mentioned above, be careful with the input you give in the x matrix and the R vector.

Value

A list including:

bols

The OLS (Ordinary Least Squares) beta coefficients.

bcls

The CLS (Constrained Least Squares) beta coefficients.

Author(s)

Michail Tsagris.

R implementation and documentation: Michail Tsagris [e-mail].

References

Hansen, B. E. (2022). Econometrics, Princeton University Press.

See Also

pls

Examples

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