pressliu {fastliu} | R Documentation |
Predicted Residual Sum of Squares (PRESS)
Description
pressliu
computes the predicted residual sum of squares (PRESS) based on a
Liu regression model.
Usage
pressliu(obj, digits = 5L, ...)
Arguments
obj |
A |
digits |
Decimal places in the columns of data frame of PRESS values. Can be an integer of vector of integers. |
... |
Not used in this implementation. |
Details
The PRESS statistic is based on the predicted leave-one-out residual sum of squares.
The statistic is computed as {\sum\limits _{i=1}^{n}\left(\frac{\hat{e}_{\lambda i}}{1-h_{1-ii}}-\frac{e_{i}\left(h_{1-ii}-\tilde{\mathbf{H}}_{\lambda-ii}\right)}{\left(1-h_{1-ii}\right)\left(1-h_{ii}\right)}\right)^{2}}
where h_{ii}
is the i
th diagonal element of the hat matrix corresponding
to the least squares estimator, h_{1-ii}
is the i
th diagonal
element of the hat matrix of the Liu estimator and e_{\lambda i}
is the residual at the specific value of \lambda
.
Value
The returned object is a vector of PRESS values computed for each lambda.
.
Author(s)
Murat Genç, Ömer Özbilen
References
Liu, K. (1993). A new class of blased estimate in linear regression. Communications in Statistics-Theory and Methods, 22(2), 393-402. doi:10.1080/03610929308831027.
Ozkale, M. R. and Kaciranlar, S. (2007). A prediction-oriented criterion for choosing the biasing parameter in Liu estimation. Communications in Statistics-Theory and Methods, 36(10), 1889-1903. doi:10.1080/03610920601126522.
See Also
liureg()
, pressliu()
, residuals()
Examples
data("Hitters")
Hitters <- na.omit(Hitters)
X <- model.matrix(Salary ~ ., Hitters)[, -1]
y <- Hitters$Salary
lam <- seq(0, 1, 0.01)
liu.mod <- liureg(X, y, lam)
pressliu(liu.mod)