Consider thefamilyofParetodistributionswithdensities with respecttostandardLebesguemeasureon R and assume > 2 butunknown. Consider asample X1, ...,Xn from thisdistribution.

Consider thefamilyofParetodistributionswithdensities

with respecttostandardLebesguemeasureon R and assume α > 2 butunknown.
Consider asample X1, ...,Xn from thisdistribution.

a) Determineamomentestimator ˜αn for α based onthestatistic t(x) = x and the sample X1, ...,Xn;

b) Findtheasymptoticdistributionofthismomentestimator;

c) ShowthattheMLE ˆαn of α based onthesample X1, ...,Xn is givenas

d) Findtheasymptoticdistributionof ˆαn;

e) Comparetheestimators ˜αn and ˆαn.

Transcribed Image Text:

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