2. V is completely known (i.e., the values of all elements of V are given). Construct an estimator of ? and discuss the statistical properties (e.g., bias, variance) of your estimator. 2. Consider the multiple regression model for \( n \) y-data \( y_1, \ldots, y_n \) (n is sample size)\[ y = X_1 B_1 + X_2 B_2 + \varepsilon \]where \( \mathbf{y} = (y_1, \ldots, y_n)' \), \( X_1 \) and \( X_2 \) are random except the intercept term (i.e., the vector of 1) included in \( X_1 \). Conditional on \( X_1 \) and \( X_2 \), the random error vector \( \varepsilon \) is jointly normal with zero expectation and variance-covariance matrix \( V \), which does not depend on \( X_1 \) and \( X_2 \). \( V \) is *not* a diagonal matrix (i.e., some off-diagonal elements are nonzero). \( B_1 \) and \( B_2 \) are vectors of two different sets of regression coefficients; \( B_1 \) has two regression coefficients and \( B_2 \) has four regression coefficients. \( B = (B'_1, B'_2)' \); that is, \( B \) is a column vector of six regression coefficients.

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

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