Constrained least squares
Constrained least squares.
cls(y, x, R, ca)
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 β = c. See details and examples. |
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 β = c. As mentioned above, be careful with the input you give in the x matrix and the R vector.
A list including:
bols |
The OLS (Ordinary Least Squares) beta coefficients. |
bcls |
The CLS (Constrained Least Squares) beta coefficients. |
Michail Tsagris
R implementation and documentation: Michail Tsagris mtsagris@uoc.gr
Hansen, B. E. (2019). Econometrics. https://www.ssc.wisc.edu/~bhansen/econometrics/Econometrics.pdf
x <- as.matrix( iris[1:50, 1:4] ) y <- rnorm(50) R <- c(1, 1, 1, 1) cls(y, x, R, 1)
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