# aul

0th

Percentile

##### Almost Unbiased Liu Estimator

aul can be used to find the Almost Unbiased Liu Estimated values and corresponding scalar Mean Square Error (MSE) value in the linear model. Further the variation of MSE can be shown graphically.

Keywords
~kwd1, ~kwd2
##### Usage
aul(formula, d, data = NULL, na.action, ...)
##### Arguments
formula
in this section interested model should be given. This should be given as a formula.
d
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 obtained the variation of scalar MSE values graphically. See Examples.

##### Value

• If d is a single numeric value then aul returns the Almost Unbiased Liu Estimated values, standard error values, t statistic values, p value and corresponding scalar MSE value. If d is a vector of set of numeric values then aul returns all the scalar MSE values and corresponding parameter values of Almost Unbiased Liu Estimator.

##### References

Akdeniz, F. and Erol, H. (2003) Mean Squared Error Matrix Comparisons of Some Biased Estimators in Linear Regression in Communications in Statistics - Theory and Methods, volume 32 DOI:10.1081/STA-120025385

plot

• aul
##### Examples
## Portland cement data set is used.
data(pcd)
d<-0.05
aul(Y~X1+X2+X3+X4-1,d,data=pcd)   # Model without the intercept is considered.

## To obtain the variation of MSE of Almost Unbiased Liu Estimator.
data(pcd)
d<-c(1:10/10)
plot(aul(Y~X1+X2+X3+X4-1,d,data=pcd),
main=c("Plot of MSE of Almost Unbiased Liu Estimator"),type="b",
points(smse[1,],pch=16,cex=0.6)