1. Consider a linear regression model y = XB+ e with E(e) = 0. The bias of the ridge estimator of obtained by minimizing Q(B) = (y - XB)¹ (y - XB) +r(BTB), for some r > 0, is -(X¹X (XTX -1 +rI)-¹B ² (X²X+rI)-¹B −r(X¹X +rI)−¹ß r(X¹X+r1) ¹8

MATLAB: An Introduction with Applications
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1. Consider a linear regression model y = X3 + e with E(e) = 0. The bias of the ridge estimator of obtained
by minimizing Q(B) = (y — Xß)¹ (y — Xß) +r(BTB), for some r > 0, is
- ²/(X²X + rI)¯¹ B
1
(X²X + rI)-¹B
r
-r(X¹X +r1) ¹8
r(X¹X +rI)¯¹ß
Transcribed Image Text:1. Consider a linear regression model y = X3 + e with E(e) = 0. The bias of the ridge estimator of obtained by minimizing Q(B) = (y — Xß)¹ (y — Xß) +r(BTB), for some r > 0, is - ²/(X²X + rI)¯¹ B 1 (X²X + rI)-¹B r -r(X¹X +r1) ¹8 r(X¹X +rI)¯¹ß
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