2. Consider a one-factor model: Y = BF + U where Y is the data N x T dimensional; B is N x 1 dimensional vector of betas; F is 1 x T dimensional vector of factors. We estimate B and F using the following method: with constraint min ||Y - BF|| B,F 7F *F'= 1 Show that the solution F/VT is the eigenvector of the Tx T matrix Y'Y.

Advanced Engineering Mathematics
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Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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2. Consider a one-factor model:
Y = BF +U
where Y is the data N x T dimensional; B is N x 1 dimensional vector of
betas; F is 1 × T dimensional vector of factors. We estimate B and F using
the following method:
min ||Y – BF||
B,F
with constraint
1
F*F= 1
Show that the solution F//T is the eigenvector of the T ×T matrix Y'Y.
Transcribed Image Text:2. Consider a one-factor model: Y = BF +U where Y is the data N x T dimensional; B is N x 1 dimensional vector of betas; F is 1 × T dimensional vector of factors. We estimate B and F using the following method: min ||Y – BF|| B,F with constraint 1 F*F= 1 Show that the solution F//T is the eigenvector of the T ×T matrix Y'Y.
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