64 ∙ without specifying the full distribution of u

Info iconThis preview shows pages 64–67. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 64 ∙ Without specifying the full distribution of U we cannot know the full conditional distribution, D Y | X . But at least we know the mean and variance (if we know , , and U 2 ). ∙ All of the findings for variances values of linear combinations of vectors have extensions to conditional variances. 65 ( cv5 ) If A x is an r m function and b x and m 1 function then Var A X Y b X | X A X Var Y | X A X ′ ∙ As a special case, Var a X ′ Y b X | X a X ′ Var Y | X a X where a X is an m 1 vector. We can write this out as Var a 1 X Y 1 a 2 X Y 2 ... a m X Y m b X | X ∑ i 1 m a i X 2 Var Y i | X 2 ∑ i 1 m − 1 ∑ j i 1 m a i X a j X Cov Y i , Y j | X 66 ∙ If Cov Y i , Y j | X 0, all i ≠ j then Var ∑ i 1 m a i X Y i X ∑ i 1 m a i X 2 Var Y i | X ∙ As a special case of this, with a i X ≡ 1, Var ∑ i 1 m Y i X ∑ i 1 m Var Y i | X just like in the case of unconditional variances. 67...
View Full Document

{[ snackBarMessage ]}

Page64 / 67

64 ∙ Without specifying the full distribution of U we...

This preview shows document pages 64 - 67. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online