2. Consider the multiple regression model for n y-data yı, ., Yn, (n is sample size) y = X,B, + X,B2 + ɛ where y = (y1, .., yn)', X1 and X2 are random except the intercept term (i.e., the vector of 1) included in X1. Conditional on X1 and X2, the random error vector ɛ is jointly normal with zero expectation and variance-covariance matrix V, which does not depend on X1 and X2. V is not a diagonal matrix (i.e., some off-diagonal elements are nonzero). B1 and B2 are vectors of two different sets of regression coefficients; B1 has two regression coefficients and B2 has four regression coefficients. B = = (B1 , B½)'; that is, B is a column vector of six regression coefficients
2. Consider the multiple regression model for n y-data yı, ., Yn, (n is sample size) y = X,B, + X,B2 + ɛ where y = (y1, .., yn)', X1 and X2 are random except the intercept term (i.e., the vector of 1) included in X1. Conditional on X1 and X2, the random error vector ɛ is jointly normal with zero expectation and variance-covariance matrix V, which does not depend on X1 and X2. V is not a diagonal matrix (i.e., some off-diagonal elements are nonzero). B1 and B2 are vectors of two different sets of regression coefficients; B1 has two regression coefficients and B2 has four regression coefficients. B = = (B1 , B½)'; that is, B is a column vector of six regression coefficients
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Consider the case that the values of V are not completely given.
Construct an estimator of B and derive its variance-
Can the variance-covariance matrix be unbiasedly estimated?
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