aul: Almost Unbiased Liu Estimator In lrmest: Different Types of Estimators to Deal with Multicollinearity

Description

`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.

Usage

 `1` ```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.

Author(s)

P.Wijekoon, A.Dissanayake

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`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15``` ```## 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", cex.lab=0.6,adj=1,cex.axis=0.6,cex.main=1, las=1,lty=3,cex=0.6) mseval<-data.frame(aul(Y~X1+X2+X3+X4-1,d,data=pcd)) smse<-mseval[order(mseval[,2]),] points(smse[1,],pch=16,cex=0.6) ```