# alte1

0th

Percentile

##### Type (1) Adjusted Liu Estimator

This function can be used to find the Type (1) Adjusted Liu Estimated values, corresponding scalar Mean Square Error (MSE) value and Prediction Sum of Square (PRESS) value in the linear model. Further the variation of MSE and PRESS values can be shown graphically.

Keywords
~kwd1, ~kwd2
##### Usage
alte1(formula, k, d, aa, press = FALSE, data = NULL, na.action, ...)
##### Arguments
formula
in this section interested model should be given. This should be given as a formula.
k
a single numeric value or a vector of set of numeric values. See Examples.
d
a single numeric value or a vector of set of numeric values. See Examples.
aa
this is a set of scalars belongs to real number system. Values for aa should be given as a vector, format. See Details.
press
if press=TRUE then all the PRESS values and its corresponding parameter values are returned. Otherwise all the scalar MSE values and its corresponding parameter values are returned.
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. In order to get the best results, optimal values for k,d and aa should be selected. The way of finding aa can be determined from Rong,Jian-Ying (2010) Adjustive Liu Type Estimators in linear regression models in communication in statistics-simulation and computation, volume 39 Use matplot so as to obtain the variation of scalar MSE values and PRESS values graphically. See Examples.

##### Value

• If k and d are single numeric values then alte1 returns the Type (1) Adjusted Liu Estimated values, standard error values, t statistic values, p value, corresponding scalar MSE value and PRESS value. If k and d are vector of set of numeric values then alte1 returns the matrix of scalar MSE values and if press=TRUE then alte1 returns the matrix of PRESS values of Type (1) Adjusted Liu Estimator by representing k and d as column names and row names respectively.

##### References

Rong,Jian-Ying (2010) Adjustive Liu Type Estimators in linear regression models in communication in statistics-simulation and computation, volume 39 DOI:10.1080/03610918.2010.484120

matplot

• alte1
##### Examples
## Portland cement data set is used.
data(pcd)
k<-0.1650
d<--0.1300
aa<-c(0.958451,1.021155,0.857821,1.040296)
alte1(Y~X1+X2+X3+X4-1,k,d,aa,data=pcd)     # Model without the intercept is considered.

## To obtain the variation of MSE of Type (1) Adjusted Liu Estimator.
data(pcd)
k<-c(0:5/10)
d<-c(5:20/10)
aa<-c(0.958451,1.021155,0.857821,1.040296)
msemat<-alte1(Y~X1+X2+X3+X4-1,k,d,aa,data=pcd)
matplot(d,alte1(Y~X1+X2+X3+X4-1,k,d,aa,data=pcd),type="l",ylab=c("MSE"),
main=c("Plot of MSE of Type (1) Adjusted Liu Estimator"),
## Use "press=TRUE" to obtain the variation of PRESS of Type (1) Adjusted Liu Estimator.