# Ordinary Generalized Stochastic Restricted Ridge Estimator This function can be used to find the Ordinary Generalized Stochastic Restricted Ridge Estimated values and corresponding scalar Mean Square Error (MSE) value. Further the variation of MSE can be shown graphically. ```r ogsrre(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 Examples . - `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 . ## Returns If `k` is a single numeric values then `ogsrre` returns the Ordinary Generalized Stochastic Restricted Ridge 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 `ogsrre` returns all the scalar MSE values and corresponding parameter values of Ordinary Generalized Stochastic Restricted Ridge Estimator. ## References Arumairajan, S. and Wijekoon, P. (2015) ] **Optimal Generalized Biased Estimator in Linear Regression Model** in **Open Journal of Statistics**, pp. 403--411 Revan, M. (2009) **A stochastic restricted ridge regression estimator** in **Journal of Multivariate Analysis**, volume 100 , issue 8, pp. 1706--1716 ## Author(s) P.Wijekoon, A.Dissanayake ## See Also `plot` ## Examples ```r ## 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) ogsrre(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 Stochastic # Restricted Ridge 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(ogsrre(Y~X1+X2+X3+X4-1,r,R,dpn,delt,k,data=pcd), main=c("Plot of MSE of Ordinary Generalized Stochastic Restricted Ridge 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(ogsrre(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) ```

ogsrre function