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Consider the regression model Y₁ = ẞX; +u₁ Where u; and X, satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ= where Y and X are the sample means of Y, and X,, respectively. Show that ẞ is a linear function of Y₁, Y2.... Y Show that ẞ is conditionally unbiased. 1. E(XXX)= 2017-0 2. E(X₁. X2...X) = E Y -Yn) B X X2..... Xn)

Consider the regression model Y₁ = ẞX; +u₁ Where u; and X, satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ= where Y and X are the sample means of Y, and X,, respectively. Show that ẞ is a linear function of Y₁, Y2.... Y Show that ẞ is conditionally unbiased. 1. E(XXX)= 2017-0 2. E(X₁. X2...X) = E Y -Yn) B X X2..... Xn)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Consider the regression model Y₁ = ẞX; +u₁ Where u; and X, satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ= where Y and X are the sample means of Y, and X,, respectively. Show that ẞ is a linear function of Y₁, Y2.... Y Show that ẞ is conditionally unbiased. 1. E(XXX)= 2017-0 2. E(X₁. X2...X) = E Y -Yn) B X X2..... Xn)
Transcribed Image Text:Consider the regression model Y₁ = ẞX; +u₁ Where u; and X, satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ẞ= where Y and X are the sample means of Y, and X,, respectively. Show that ẞ is a linear function of Y₁, Y2.... Y Show that ẞ is conditionally unbiased. 1. E(XXX)= 2017-0 2. E(X₁. X2...X) = E Y -Yn) B X X2..... Xn)
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