optimum
Summary of optimum scalar Mean Square Error values of all estimators and optimum Prediction Sum of Square values of some of the estimators
optimum
can be used to obtain the optimal scalar Mean Square Error (MSE) values and its corresponding parameter values (k
and/or d
) of all estimators and the optimum Prediction Sum of Square (PRESS) values and its corresponding parameter values k
and d
of some of the estimators considered in this package.
Usage
optimum(formula , r, R, dpn, delt, aa1, aa2, aa3, k, d, press = FALSE, 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 avector
or amatrix
. 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 avector
or amatrix
. 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 avector
(only the diagonal elements) or amatrix
. See ‘Examples’.  delt

values of $E(r)  R\beta$ and that should be given as either a
vector
or amatrix
. See ‘Examples’.  aa1

adjusted parameters of Type (1) Adjusted Liu Estimators and that should be a set of scalars belongs to real number system. Values for “aa1” should be given as a
vector
, format. See ‘Details’.  aa2

adjusted parameters of Type (2) Adjusted Liu Estimators and that should be a set of scalars belongs to real number system. Values for “aa2” should be given as a
vector
, format. See ‘Details’.  aa3

adjusted parameters of Type (3) Adjusted Liu Estimators and that should be a set of scalars belongs to real number system. Values for “aa3” should be given as a
vector
, format. See ‘Details’.  k
 a vector of set of numeric values. See ‘Examples’.
 d
 a vector of set of numeric values. See ‘Examples’.
 press

an optional object specifying the PRESS values. That is, if “press=TRUE” then summary of PRESS of some of the estimators are returned with corresponding
k
andd
values. Otherwise summary of scalar MSE of all estimators are returned with correspondingk
and/ord
values.  data

an optional data frame, list or environment containing the variables in the model. If not found in
data
, the variables are taken fromenvironment(formula)
, typically the environment from which the function is called.  na.action

if the dataset contain
NA
values, thenna.action
indicate what should happen to thoseNA
values.  ...
 currently disregarded.
Details
Since formula has an implied intercept term, use either y ~ x  1
or y ~ 0 + x
to remove the intercept.
Optimum scalar MSE values of all estimators can be found for a given range of parameters. Hence the best estimator can be found based on the MSE criteria. Further prior information should be given in order to obtained the results.
The way of finding aa1
, aa2
and aa3
can be determined from Rong,JianYing, (2010), Adjustive Liu Type Estimators in linear regression models in communication in statisticssimulation and computation, volume 39
Value

By default,
optimum
returns the optimum scalar MSE values and corresponding parameter values of all estimators. If “press=TRUE” then optimum
return the optimum PRESS values and corresponding parameter values of some of the estimators.
Note
Conversion of estimators and corresponding k
and/or d
values are given below.
SRRE = MIXE k=0
OGSRRE = MIXE k=0
RE = OLS k=0
OGRE = OLS k=0
RLE = RLS d=1
OGRLE = RLS d=1
LE = OLS d=1
OGLE = OLS d=1
RRRE = RLS k=0
OGRRRE = RLS k=0
SRLE = MIXE d=1
OGSRLE = MIXE d=1
AURE = OLS k=0
OGAURE = OLS k=0
AULE = OLS d=1
OGAULE = OLS d=1
LTE1 = RE d=0
OGLTE1 = RE d=0
LTE1 = OLS k=0 and d=0
OGLTE1 = OLS k=0 and d=0
LTE2 = RE d=0
OGLTE2 = RE d=0
LTE2 = OLS k=0 and d=0
OGLTE2 = OLS k=0 and d=0
Examples
## portland cement data set is used.
data(pcd)
attach(pcd)
k<c(0:3/10)
d<c(3:3/10)
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)
aa1<c(0.958451,1.021155,0.857821,1.040296)
aa2<c(0.345454,1.387888,0.866466,1.354454)
aa3<c(0.344841,1.344723,0.318451,1.523316)
optimum(Y~X1+X2+X3+X41,r,R,dpn,delt,aa1,aa2,aa3,k,d,data=pcd)
# Model without the intercept is considered.
## Use "press=TRUE" to get the optimum PRESS values only for some of the estimators.