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et be an unknown population parameter associated with the collection of observations (X₁, Y₁), (X2, Y₂), ..., (Xn, Yn) here, for €1, €2,..., En iid N(0,0²), Y₁ = BX₁ + €₁, for i=1,2,..., n. This similar to the regression model we examined in class, but without the intercept term this question, we are going to derive the regression estimator for the model, using the same pproach from the lecture.

et be an unknown population parameter associated with the collection of observations (X₁, Y₁), (X2, Y₂), ..., (Xn, Yn) here, for €1, €2,..., En iid N(0,0²), Y₁ = BX₁ + €₁, for i=1,2,..., n. This similar to the regression model we examined in class, but without the intercept term this question, we are going to derive the regression estimator for the model, using the same pproach from the lecture.

MATLAB: An Introduction with Applications
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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Let be an unknown population parameter associated with the collection of observations (X₁,Y₁), (X2, Y₂), ..., (Xn, Yn) iid where, for €1, €2,..., En ~ N(0,0²), Y₁ = 3X₁ + €₁, for i=1,2,..., n. This similar to the regression model we examined in class, but without the intercept term In this question, we are going to derive the regression estimator for the model, using the same approach from the lecture.
Transcribed Image Text:Let be an unknown population parameter associated with the collection of observations (X₁,Y₁), (X2, Y₂), ..., (Xn, Yn) iid where, for €1, €2,..., En ~ N(0,0²), Y₁ = 3X₁ + €₁, for i=1,2,..., n. This similar to the regression model we examined in class, but without the intercept term In this question, we are going to derive the regression estimator for the model, using the same approach from the lecture.
1. Write down the log-likelihood function for €1, €2,..., En based on the pdf of N(0, ²), i.e., derive the expression for: Using this answer and the fact that l(0²) = [log ƒ(€₁; 0²) i=1 €₁ = Y₁ - 0X₁, derive the expression for the log-likelighood function w.r.t. the unknown parameters (0,0²), i.e., n l(0,0²) = log f(Xi, Yi; 0,0²) i=1
Transcribed Image Text:1. Write down the log-likelihood function for €1, €2,..., En based on the pdf of N(0, ²), i.e., derive the expression for: Using this answer and the fact that l(0²) = [log ƒ(€₁; 0²) i=1 €₁ = Y₁ - 0X₁, derive the expression for the log-likelighood function w.r.t. the unknown parameters (0,0²), i.e., n l(0,0²) = log f(Xi, Yi; 0,0²) i=1
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