Consider the regression model Y₁ = ẞX; +u; Where ui and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ß: = Show that ẞ is a linear function of Y₁, Y2,..., Y. ☑' where Y and X are the sample means of Y; and X;, respectively. 1 +Yn) Show that ẞ is conditionally unbiased. 1. E(YX1, X2 Xn) = BX (@K}6, +Yn) +X₂+...+Xn) = B 2. E(BIX1, X2,..., Xn) = E || (x₁₁ X 2...., Xn) D
Consider the regression model Y₁ = ẞX; +u; Where ui and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ß: = Show that ẞ is a linear function of Y₁, Y2,..., Y. ☑' where Y and X are the sample means of Y; and X;, respectively. 1 +Yn) Show that ẞ is conditionally unbiased. 1. E(YX1, X2 Xn) = BX (@K}6, +Yn) +X₂+...+Xn) = B 2. E(BIX1, X2,..., Xn) = E || (x₁₁ X 2...., Xn) D
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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Transcribed Image Text:Consider the regression model
Y₁ = ẞX; +u;
Where
ui
and X; satisfy the assumptions specified here. Let ẞ denote an estimator of ẞ that is constructed as ß:
=
Show that ẞ is a linear function of Y₁, Y2,..., Y.
☑'
where Y and X are the sample means of Y; and X;, respectively.
1
+Yn)
Show that ẞ is conditionally unbiased.
1. E(YX1, X2 Xn) = BX
(@K}6,
+Yn)
+X₂+...+Xn) = B
2. E(BIX1, X2,..., Xn) = E
|| (x₁₁ X 2...., Xn)
D
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