statliu {fastliu}

Liu Regression Statistics

Description

statliu computes the statistics related to the Liu regression.

Usage

statliu(obj)

Arguments

obj

An object of class liureg.

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.

Value

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

Author(s)

Murat Genç

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.

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)