5. Consider the linear regression model with assumptions (i) to (iii) and (iv*). ((X'V-'x)-x'v-)y. 1 -y' (In n - p (a) Show that ô? can be written as o (b) Show that E(ô?) = o² for every (B, o2) E R' x (0, 00).
5. Consider the linear regression model with assumptions (i) to (iii) and (iv*). ((X'V-'x)-x'v-)y. 1 -y' (In n - p (a) Show that ô? can be written as o (b) Show that E(ô?) = o² for every (B, o2) E R' x (0, 00).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:5. Consider the linear regression model with assumptions (i) to (iii) and (iv*).
1
y'(In - X(X'V-lX)-x'v-1)y .
п — р
(a) Show that ô can be written as 6
(b) Show that E(ô?) = o² for every (B,o²) E Rº × (0, 0).
Assumptions
(i) X is a non-stochasticn x p matrix with p < n;
(ii) the matrix X has rank p, i.e. X is of full column rank;
(iii) the elements of the n x 1 vector y are observable random vectors;
(iv*) the elements of the n x 1 vector e are non-observable random vari-
ables such that E(e) = 0 and Cov(e) = o²V, where V is a known
n x n symmetric positive definite matrix and o? > 0 is an unknown parameter.
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