Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Library: eiv
See also: eivvec2

Macro: eivvec1
Description: eivvect1 presents the maximum likelihood estimators of the parameters in the measurement error models, which has more than one variable x. The covariances between e and u, Sigeu and the covariance matrix of u, Sigu are known. All of the variables obey normal distributions. All parameters are estimated by maximum likelihood method in measurement error models, see Fuller W. A. "Measurement Error Models", Wiley and Sons 1987, section 2.2.

Link:
Usage: {mux,hatbeta,beta0,hatsigmae,hatsigmax)=eivvec1(X,Y,Sigue,Sigu)
Input:
X n x p matrix, the design variables
Y n x 1 matrix, the response
Sigue p x 1 matrix, the vector of covariances between u and e
Sigu p x p matrix, the covariance matrix of u
Output:
mux scalar, the mean value of X
hatbeta1 vector, the estimate
hatbeta0 scalar, the estimate
hatsigmax p x p matrix, the estimate of the covariance matrix of X
hatsigmae scalar, the estimate of the variance of error e

Example:
library("eiv")
library("xplore")
n = 100
randomize(n)
nu =#(2,3,4)
sig=0*matrix(3,3)
sig[,1]=#(0.25, 0.9, 0.1)
sig[,2]=#(0.9, 1, 0.2)
sig[,3]=#(0.1, 0.2, 4)
x=normal(n,3)*sig+nu'
X =x+0.01*normal(n,3)
a1=#(1.2, 1.3, 1.4)
Y =0.75+X*a1+0.09*normal(n)
Sigue=#(0.11, 0.09, 045)
Sigu=0*matrix(3,3)
Sigu[,1]=#(1.25, 0.009, 0.01)
Sigu[,2]=#(0.009,0.081, 0.02)
Sigu[,3]=#(0.01, 0.02, 1.96)
gest=eivvec1(X,Y,Sigue,Sigu)
gest.mux
gest.hatbeta
gest.beta0
gest.hatsigmax
gest.hatsigmae
Result:
gest.mux=(2.024, 2.9106, 3.9382) 
gest.hatbeta=(1.1387, 1.3217, 1.3852)
gest.beta0=0.87062
gest.hatsigmax=(0.84466, 1.0319, 0.43677
1.0319,  1.664,  1.0941
0.43677, 1.0941, 19.781)
gest.hatsigmae=1034.9

Library: eiv
See also: eivvec2

Keywords - Function groups - @ A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

Author: Hua Liang, 970725
(C) MD*TECH Method and Data Technologies, 28.6.1999