2 Consider the linear regression model Y₁ = x + εi (i= 1,..., n) wherea, is a k x 1 vector of regressors, B is the kx 1 vector of unknown parameters and ₁ is the unobservable error term. Assume that the random vector w; = [yi, is i.i.d. and that E (x₁) = 0. Let B = (1) ydenote the least squares estimator for B. (a) Quoting any additional assumptions that you find appropriate, show that is consistent for B.
2 Consider the linear regression model Y₁ = x + εi (i= 1,..., n) wherea, is a k x 1 vector of regressors, B is the kx 1 vector of unknown parameters and ₁ is the unobservable error term. Assume that the random vector w; = [yi, is i.i.d. and that E (x₁) = 0. Let B = (1) ydenote the least squares estimator for B. (a) Quoting any additional assumptions that you find appropriate, show that is consistent for B.
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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![2 Consider the linear regression model
Yi = xß + εi (i = 1,..., n)
where x, is a k x 1 vector of regressors, ß is the kx 1 vector of unknown parameters and Ei
is the unobservable error term. Assume that the random vector w; = [yi, x is i.i.d. and
that E (x₁) = 0. Let B = (₁₁) iyi denote the least squares estimator
for B.
(a) Quoting any additional assumptions that you find appropriate, show that B is consistent
for B.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b1c41e0-1a01-40ab-ae2e-a82ae6dd7ed0%2F75c00562-5c0c-41e1-b81f-cc6375c3b1c1%2Fap3cm0r_processed.png&w=3840&q=75)
Transcribed Image Text:2 Consider the linear regression model
Yi = xß + εi (i = 1,..., n)
where x, is a k x 1 vector of regressors, ß is the kx 1 vector of unknown parameters and Ei
is the unobservable error term. Assume that the random vector w; = [yi, x is i.i.d. and
that E (x₁) = 0. Let B = (₁₁) iyi denote the least squares estimator
for B.
(a) Quoting any additional assumptions that you find appropriate, show that B is consistent
for B.
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