Consider asample Z1, ,Zn of independentandidenticallydistrib uted randomvariables,where Zi Xi Yi with Xi and Yi independent andexpo nentially distributedwithmean a) Determineamomentestimator of based onthestatistic t(z) z2 b) Showthatifwealsohadobservedbothof Xi and Yi, theMLEwouldbe c) Comparethee...

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Consider asample Z1, ...,Zn of independentandidenticallydistrib- uted randomvariables,where Zi = Xi Yi with Xi and Yi

Question:

Consider asample Z1, ...,Zn of independentandidenticallydistrib-

uted randomvariables,where Zi = Xi − Yi with Xi and Yi independent andexpo-

nentially distributedwithmean θ.

a) Determineamomentestimator ˜θ of θ based onthestatistic t(z) = z2.

b) Showthatifwealsohadobservedbothof Xi and Yi, theMLEwouldbe

image text in transcribed

c) Comparetheestimators ˜θ and ˆθ via asuitablesimulationstudy.

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Fundamentals Of Mathematical Statistics

ISBN: 9781032223827

1st Edition

Authors: Steffen Lauritzen

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Question Posted: Sep 19, 2024 08:00 PM

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Consider asample Z1, ...,Zn of independentandidenticallydistrib- uted randomvariables,where Zi = Xi Yi with Xi and Yi

Question:

2n (Xi+Y); i=1

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Fundamentals Of Mathematical Statistics

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