Under the linear model assumption, let there be two random vectors that will be the estimators of B: B B Also, assume that .cov(ß) < cov(ß) a. Prove that the following expressions are equivalent to one another: Vw e RP, Var(w") < V ar(w"3) b. Prove that the following matrix is positive semi-definite: cov(ß) – cov(B)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Under the linear model assumption, let there be two random vectors that will be the
estimators of B: B B
Also, assume that .cov(B) < cov(ß)
a. Prove that the following expressions are equivalent to one another:
Vw e RP, Var(w"ß) < Var(wTB)
b. Prove that the following matrix is positive semi-definite:
cov (3) – cov(B)
Transcribed Image Text:Under the linear model assumption, let there be two random vectors that will be the estimators of B: B B Also, assume that .cov(B) < cov(ß) a. Prove that the following expressions are equivalent to one another: Vw e RP, Var(w"ß) < Var(wTB) b. Prove that the following matrix is positive semi-definite: cov (3) – cov(B)
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