5.4.14. Let Y1, Y2, ... , Yn be a random sample of size n from the pdf fy(y; 0) = ¿e¬y/®, y > 0. Let ô = n · Ymin- Is ê unbiased for 0? Is ô = ;£Y; unbiased for 0? i=1

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An introduction to Mathematical Statistics and Its Applications by Richard J. Larsen, Morris L. Marx (z-lib.org).pdf (page 324 of 753)
ΣΤ-μ unDIaseαΤΟ σ.
|
i=1
on
5.4.13. As an alternative to imposing unbiasedness, an es-
timator's distribution can be "centered" by requiring that
its median be equal to the unknown parameter 0. If it is,
ê is said to be median unbiased. Let Y1, Y2, . , Yn be a
random sample of size n from the uniform pdf, fy (y;0) =
1/0, 0 < y < 0. For arbitrary n, is Ô = "+l.Ymax median
unbiased? Is it median unbiased for any value of n?
66
in
0.
312
lom
ver
sed
hat
5.4.14. Let Y1, Y2, . . , Yn be a random sample of sizen
from the pdf fy(y;0) = ¿e-y/®, y > 0. Let = n· Ymin- Is
bar-
ê unbiased for 0? Is ô = !> Y; unbiased for 0?
%3D
n
i=1
313
ow
ven
he?
h(W1, ., Wn) is said to be
O i lim EÔ.
5 4.15. An estimator 0,
Sunn
Transcribed Image Text:File eitVie Tools Window Help Thu 11:28 PM An introduction to Mathematical Statistics and Its Applications by Richard J. Larsen, Morris L. Marx (z-lib.org).pdf (page 324 of 753) ΣΤ-μ unDIaseαΤΟ σ. | i=1 on 5.4.13. As an alternative to imposing unbiasedness, an es- timator's distribution can be "centered" by requiring that its median be equal to the unknown parameter 0. If it is, ê is said to be median unbiased. Let Y1, Y2, . , Yn be a random sample of size n from the uniform pdf, fy (y;0) = 1/0, 0 < y < 0. For arbitrary n, is Ô = "+l.Ymax median unbiased? Is it median unbiased for any value of n? 66 in 0. 312 lom ver sed hat 5.4.14. Let Y1, Y2, . . , Yn be a random sample of sizen from the pdf fy(y;0) = ¿e-y/®, y > 0. Let = n· Ymin- Is bar- ê unbiased for 0? Is ô = !> Y; unbiased for 0? %3D n i=1 313 ow ven he? h(W1, ., Wn) is said to be O i lim EÔ. 5 4.15. An estimator 0, Sunn
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