# ogrrre

0th

Percentile

##### Ordinary Generalized Restricted Ridge Regression Estimator

This function can be used to find the Ordinary Generalized 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
ogrrre(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 Example.
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 ogrrre returns the Ordinary Generalized 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 ogrrre returns all the scalar MSE values and corresponding parameter values of Ordinary Generalized Restricted Ridge Regression Estimator.

##### References

Arumairajan, S. and Wijekoon, P. (2015) ] Optimal Generalized Biased Estimator in Linear Regression Model in Open Journal of Statistics, pp. 403--411 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

• ogrrre
##### 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)
ogrrre(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 Ordinary Generalized 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(ogrrre(Y~X1+X2+X3+X4-1,r,R,dpn,delt,k,data=pcd),
main=c("Plot of MSE of Ordinary Generalized Restricted Ridge Regression
points(smse[1,],pch=16,cex=0.6)