# rrre

0th

Percentile

##### Restricted Ridge Regression Estimator

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

Keywords
~kwd1, ~kwd2
##### Usage
rrre(formula, r, R, dpn, delt, k, 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.
dpn
dispersion matrix of vector of disturbances of linear restricted model, $r = R\beta + \delta + \nu$. Values for dpn should be given as either a vector (only the diagonal elements) 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.
k
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 k is a single numeric values then rrre returns the Restricted Ridge Regression Estimated values, standard error values, t statistic values, p value and corresponding scalar MSE value. If k is a vector of set of numeric values then rrre returns all the scalar MSE values and corresponding parameter values of Restricted Ridge Regression Estimator.

##### References

Sarkara, N. (1992), A new estimator combining the ridge regression and the restricted least squares methods of estimation in Communications in Statistics - Theory and Methods, volume 21, pp. 1987--2000. DOI:10.1080/03610929208830893

plot

• rrre
##### Examples
## Portland cement data set is used.
data(pcd)
k<-0.05
r<-c(2.1930,1.1533,0.75850)
R<-c(1,0,0,0,0,1,0,0,0,0,1,0)
dpn<-c(0.0439,0.0029,0.0325)
delt<-c(0,0,0)
rrre(Y~X1+X2+X3+X4-1,r,R,dpn,delt,k,data=pcd)
# Model without the intercept is considered.

## To obtain variation of MSE of Restricted Ridge Regression Estimator.
data(pcd)
k<-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)
dpn<-c(0.0439,0.0029,0.0325)
delt<-c(0,0,0)
plot(rrre(Y~X1+X2+X3+X4-1,r,R,dpn,delt,k,data=pcd),
main=c("Plot of MSE of Restricted Ridge Regression Estimator"),
points(smse[1,],pch=16,cex=0.6)