2. Consider the multiple regression model for n y-data yı, .., Yn, (n is sample size) y = X,B1 + X2B2 + ɛ where y = (y1,..., yn)', X1 and X2 are random except the intercept term (i.e., the vector of...


Consider the case that the values of V are not completely given.
 Construct an estimator of B and derive its variance-covariance matrix.
 Can the variance-covariance matrix be unbiasedly estimated?


2. Consider the multiple regression model for n y-data yı, .., Yn, (n is sample size)<br>y = X,B1 + X2B2 + ɛ<br>where y = (y1,..., yn)', X1 and X2 are random except the intercept term (i.e., the<br>vector of 1) included in X1. Conditional on X1 and X2, the random error vector<br>ɛ is jointly normal with zero expectation and variance-covariance matrix V,<br>which does not depend on X1 and X2. V is not a diagonal matrix (i.e., some<br>off-diagonal elements are nonzero). B1 and B2 are vectors of two different<br>sets of regression coefficients; B1 has two regression coefficients and B2 has<br>four regression coefficients. B = (B1 , B½)'; that is, B is a column vector of<br>%3D<br>six regression coefficients.<br>

Extracted text: 2. Consider the multiple regression model for n y-data yı, .., Yn, (n is sample size) y = X,B1 + X2B2 + 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 %3D six regression coefficients.

Jun 01, 2022
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