lrmest (version 3.0)

rls: Restricted Least Square Estimator

Description

This function can be used to find the Restricted Least Square Estimated values and corresponding scalar Mean Square Error (MSE) value.

Usage

rls(formula, r, R, delt, data, 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’.

delt

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

Value

rls returns the Restricted Least Square Estimated values, standard error values, t statistic values,p value and corresponding scalar MSE value.

Details

Since formula has an implied intercept term, use either y ~ x - 1 or y ~ 0 + x to remove the intercept.

In order to find the results of Restricted Least Square Estimator, prior information should be specified.

References

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

Examples

## Portland cement data set is used.
data(pcd)
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)
rls(Y~X1+X2+X3+X4-1,r,R,delt,data=pcd)    # Model without the intercept is considered.