fastliu (version 1.0)

statliu: Liu Regression Statistics

Description

statliu computes the statistics related to the Liu regression.

Usage

statliu(obj)

Value

The return object is the statistics related to the Liu regression.

Arguments

obj

An object of class liureg.

Author

Murat Genç

Details

EDF (Liu, 1993; Hastie et al., 2009)	Effective degrees of freedom, \(n-\mathrm{trace}\left(2\mathbf{H}_\lambda\right)-\mathbf{H}_\lambda\mathbf{H}_\lambda^T\) for each \(\lambda\) where \(n\) is the number of the observations in the design matrix and \(\mathbf{H}_\lambda\) is the hat matrix of Liu regression at \(\lambda\).
sigma2	Computed \(\hat{\sigma}^2\) from the Liu regression for each \(\lambda\).
VAR	Variance from the Liu regression for each \(\lambda\).
BIAS2	Squared-bias from the Liu regression for each \(\lambda\).
MSE	Mean squared error (MSE) from the Liu regression for each \(\lambda\).
FVal	F-statistics value from the Liu regression for each \(\lambda\).
GCV	Generalized cross-validation (GCV) from the Liu regression for each \(\lambda\). The GCV is computed by \(\frac{\mathrm{SSR}_{\lambda}}{n-1-\mathrm{trace}\left(\mathbf{H}_{\lambda}\right)}\) where \(\mathrm{SSR}_{\lambda}\) is the residual sum of squares and \(\mathrm{trace}\left(\mathbf{H}_{\lambda}\right)\) is the trace of the hat matrix at corresponding value of \(\lambda\) from Liu regression.
R2	R-squared from the Liu regression for each \(\lambda\).
AdjR2	Adjusted R-squared from the Liu regression for each \(\lambda\).

References

Liu, K. (1993). A new class of blased estimate in linear regression. Communications in Statistics-Theory and Methods, 22(2), 393-402. tools:::Rd_expr_doi("10.1080/03610929308831027").

Hastie, T., Tibshirani, R., Friedman, J. H., Friedman, J. H. (2009). The elements of statistical learning: data mining, inference, and prediction (Vol. 2, pp. 1-758). New York: Springer.

See Also

liureg(), summary(), pressliu(), residuals()

Examples

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)
stats <- statliu(liu.mod)
print(stats)