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)
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
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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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)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F20b8f1cc-2b48-4810-a708-b77b998bc179%2F071b25a8-8ae8-4802-af03-8f789763e319%2F6tr3xzl_processed.jpeg&w=3840&q=75)
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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