# rliu

0th

Percentile

##### Restricted Liu Estimator

This function can be used to find the Restricted Liu Estimated values and corresponding scalar Mean Square Error (MSE) value. Further the variation of MSE can be shown graphically.

Keywords
~kwd1, ~kwd2
##### Usage
rliu(formula, r, R, delt, d, data = NULL, na.action, ...)
##### Arguments
formula
in this section interested model should be given. This should be given as a formula.
r
is a $j$ by $1$ matrix of linear restriction, $r = R\beta + \delta + \nu$. Values for r should be given as either a vector or a matrix. See
R
is a $j$ by $p$ of full row rank $j \le p$ matrix of linear restriction, $r = R\beta + \delta + \nu$. Values for R should be given as either a vector or a matrix. See Examples.
delt
values of $E(r) - R\beta$ and that should be given as either a vector or a matrix. See Examples.
d
a single numeric value or a vector of set of numeric values. See Examples.
data
an optional data frame, list or environment containing the variables in the model. If not found in data, the variables are taken from environment(formula), typically the environment from which the function is called.
na.action
if the dataset contain NA values, then na.action indicate what should happen to those NA values.
...
currently disregarded.
##### Details

Since formula has an implied intercept term, use either y ~ x - 1 or y ~ 0 + x to remove the intercept. Use plot so as to obtain the variation of scalar MSE values graphically. See Examples.

##### Value

• If d is a single numeric values then rliu returns the Restricted Liu Estimated values, standard error values, t statistic values, p value and corresponding scalar MSE value. If d is a vector of set of numeric values then rliu returns all the scalar MSE values and corresponding parameter values of Restricted Liu Estimator.

##### References

Hubert, M.H. and Wijekoon, P. (2006) Improvement of the Liu estimator in the linear regression medel, Chapter (4-8)

plot

• rliu
##### Examples
data(pcd)
d<-0.05
r<-c(2.1930,1.1533,0.75850)
R<-c(1,0,0,0,0,1,0,0,0,0,1,0)
delt<-c(0,0,0)
rliu(Y~X1+X2+X3+X4-1,r,R,delt,d,data=pcd)   # Model without the intercept is considered.

## To obtain the variation of MSE of Resticted Liu Estimator.
data(pcd)
d<-c(0:10/10)
r<-c(2.1930,1.1533,0.75850)
R<-c(1,0,0,0,0,1,0,0,0,0,1,0)
delt<-c(0,0,0)
plot(rliu(Y~X1+X2+X3+X4-1,r,R,delt,d,data=pcd),
main=c("Plot of MSE of Restricted Liu Estimator"),type="b",
points(smse[1,],pch=16,cex=0.6)