prstReg {ImpShrinkage} | R Documentation |
This function calculates the positive-rule Stein estimator. This estimator is an improved version of the Stein estimator, where only the positive part of the shrinking factor is considered. It may be calculated by
\hat{\beta}^{S+}= \hat{\beta}^{S} + (1 + d \mathcal{L}^{-1}) I(\mathcal{L} > d) (\hat{\beta}^{U} - \hat{\beta}^{R})
where I(A)
denotes an indicator function and
\hat{\beta}^{S}
is the Stein estimator; See stReg
.
\hat{\beta}^{U}
is the unrestricted estimator; See unrReg
.
\hat{\beta}^{R}
is the restricted estimator; See resReg
.
\mathcal{L}
is the test statistic. See teststat
;
d
is the shrinkage factor.
prstReg(X, y, H, h, d = NULL, is_error_normal = FALSE)
X |
Matrix with input observations, of dimension |
y |
Vector with response observations of size |
H |
A given |
h |
A given |
d |
(optional) If not provided (or set to |
is_error_normal |
logical value indicating whether the errors follow a
normal distribution. If |
The corresponding estimator of \sigma^2
is given by
s^2 = \frac{1}{n-p}(y-X\hat{\beta}^{S+})^{\top}(y - X\hat{\beta}^{S+}).
An object of class pst
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), nr = 3, nc = p, byrow = TRUE)
h <- rep(0, nrow(H))
prstReg(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), nr = 3, nc = p, byrow = TRUE)
h <- rep(1, nrow(H))
prstReg(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))
prstReg(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))
prstReg(X, y, H, h)