Description Usage Arguments Details Value Author(s) References See Also Examples
The lstats
function computes the Liu regression related statistics such as variance, estimated squared bias, MSE, R-squared and adjusted R-squared etc. These statistics are computed by following Liu (1993) <doi:10.1080/03610929308831027>; Akdeniz, F. and Kaciranlar, S. (1995) <doi:10.1080/03610929508831585>; Cule, E. and De Iorioa, M. (2012); Hastie, T. and Tibshirani, R. (1990); and Mallows (1973) <doi:10.2307/1267380>.
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object |
An object of class "liu". |
x |
An object of class "liu" for |
... |
Not presently used in this implementation. |
The lstats
function computes the Liu regression related statistics which may help in selecting appropriate optimal value of biasing parameter d. If value of d is one then these statistics are equivalent to the relevant OLS statistics.
lEDF |
Residual effective degrees of freedom for given biasing parameter d from Hastie and Tibshirani (1990), i.e., n-trace(2H_d)-H_d t(H_d). |
lsigma2 |
Computation of \hat{σ}^2 from Liu regression. |
Cl |
Mallows C_p like statistics for given biasing parameter d. |
var |
Variance of Liu regression for given biasing parameter d. |
bias2 |
Estimated squared bias of Liu regression for given biasing parameter d. |
mse |
Total MSE value for given biasing parameter d. |
Fv |
F-statistics value for testing of the significance of the Liu regression estimator computed for given biasing parameter d. |
R2 |
R-squared for given biasing parameter d. |
adjR2 |
Adjusted R-squared for given biasing parameter d. |
minmse |
Minimum MSE value for a certain value of biasing parameter d. |
SSER |
Sum of squares of error from Liu regression for each biasing parameter d. |
Muhammad Imdad Ullah, Muhammad Aslam
Akdeniz, F. and Kaciranlar, S. (1995). On the Almost Unbiased Generalized Liu Estimators and Unbiased Estimation of the Bias and MSE. Communications in Statistics-Theory and Methods, 24, 1789–1897. http://doi.org/10.1080/03610929508831585.
Cule, E. and De lorioa, M. (2012). A semi-Automated method to guide the choice of ridge parameter in ridge regression. arXiv:1205.0686v1[stat.AP]. https://arxiv.org/abs/1205.0686v1.
Hastie, T. and Tibshirani, R. (1990). Generalized Additive Models. Chapman \& Hall.
Imdad, M. U. (2017). Addressing Linear Regression Models with Correlated Regressors: Some Package Development in R (Doctoral Thesis, Department of Statistics, Bahauddin Zakariya University, Multan, Pakistan).
Imdadullah, M., Aslam, M., and Altaf, S. (2017). liureg: A comprehensive R Package for the Liu Estimation of Linear Regression Model with Collinear Regressors. The R Journal, 9 (2), 232–247.
Liu, K. (1993). A new Class of Biased Estimate in Linear Regression. Journal of Statistical Planning and Inference, 141, 189–196. http://doi.org/10.1080/03610929308831027.
Mallows, C. L. (1973). Some Comments on Cp. Technometrics, 15: 661–675. http://doi.org/10.2307/1267380.
Liu model fitting liu
, Liu residuals residuals.liu
, Liu PRESS press.liu
, Testing of Liu Coefficients summary.liu
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