# ogrrre

##### 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.

##### 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`

. SeeExamples . - 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`

. SeeExamples - delt
- values of $E(r) - R\beta$ and that should be given as either a
`vector`

or a`matrix`

. SeeExamples . - 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

##### 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

##### See Also

##### 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
Estimator"),type="b",cex.lab=0.6,adj=1,cex.axis=0.6,cex.main=1,las=1,lty=3,cex=0.6)
mseval<-data.frame(ogrrre(Y~X1+X2+X3+X4-1,r,R,dpn,delt,k,data=pcd))
smse<-mseval[order(mseval[,2]),]
points(smse[1,],pch=16,cex=0.6)
```

*Documentation reproduced from package lrmest, version 3.0, License: GPL-2 | GPL-3*