resReg {ImpShrinkage} | R Documentation |
This function calculates the restricted estimator using
\hat{\beta}^{R} = \hat{\beta}^{U} - (X^{\top}X)^{-1}H^{\top}
(H(X^{\top}X)^{-1}H^{\top})^{-1}(H\hat{\beta}^{U}-h)
where
\hat{\beta}^{U}
is the unrestricted estimator; See unrReg
.
H\beta = h
represents a subspace of the parameter space induced
by the non-sample information. Here, H
is a known q \times p
matrix, and h
is a known q
-vector.
resReg(X, y, H, h)
X |
Matrix with input observations, of dimension |
y |
Vector with response observations of size |
H |
A given |
h |
A given |
#' The corresponding estimator of \sigma^2
is
s^2 = \frac{1}{n-p}(y-X\hat{\beta}^{R})^{\top}(y - X\hat{\beta}^{R}).
An object of class restricted
is a list containing at least the following components:
coef
A named vector of coefficients.
residuals
The residuals, that is, the response values minus fitted values.
s2
The estimated variance.
fitted.values
The fitted values.
Saleh, A. K. Md. Ehsanes. (2006). Theory of Preliminary Test and Stein‐Type Estimation With Applications, Wiley.
Kaciranlar, S., Akdeniz, S. S. F., Styan, G. P. & Werner, H. J. (1999). A new biased estimators in linear regression and detailed analysis of the widely-analysed dataset on portland cement. Sankhya, Series B, 61(3), 443-459.
Kibria, B. M. Golam (2005). Applications of Some Improved Estimators in Linear Regression, Journal of Modern Applied Statistical Methods, 5(2), 367- 380.
n_obs <- 100
p_vars <- 5
beta <- c(2, 1, 3, 0, 5)
simulated_data <- simdata(n = n_obs, p = p_vars, beta)
X <- simulated_data$X
y <- simulated_data$y
p <- ncol(X)
# H beta = h
H <- matrix(c(1, 1, -1, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0), nrow = 3, ncol = p, byrow = TRUE)
h <- rep(0, nrow(H))
resReg(X, y, H, h)
# H beta != h
H <- matrix(c(1, 1, -1, 0, 0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0), nrow = 3, ncol = p, byrow = TRUE)
h <- rep(1, nrow(H))
resReg(X, y, H, h)
data(cement)
X <- as.matrix(cbind(1, cement[, 1:4]))
y <- cement$y
# Based on Kaciranlar et al. (1999)
H <- matrix(c(0, 1, -1, 1, 0), nrow = 1, ncol = 5, byrow = TRUE)
h <- rep(0, nrow(H))
resReg(X, y, H, h)
# Based on Kibria (2005)
H <- matrix(c(0, 1, -1, 1, 0, 0, 0, 1, -1, -1, 0, 1, -1, 0, -1), nrow = 3, ncol = 5, byrow = TRUE)
h <- rep(0, nrow(H))
resReg(X, y, H, h)