1. Consider a linear regression model y = X3 + e with E(e) = 0. The bias of the ridge estimator of obtainedby minimizing Q(B) = (y — Xß)¹ (y — Xß) +r(BTB), for some r > 0, is- ²/(X²X + rI)¯¹ B1(X²X + rI)-¹Br-r(X¹X +r1) ¹8r(X¹X +rI)¯¹ß

To find the bias of the ridge estimator of β obtained by minimizing Q(β), we need to calculate the…

Answered: 1. Consider a linear regression model y…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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