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

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

nentially distributedwithmean θ.

a) Showthat Eθ(Z4 i ) =24θ4;

b) Findtheasymptoticdistributionofthemomentestimator ˜θn of θ based onthe statistic t(z) = z2;

c) Comparetheasymptoticdistributionof ˜θn to thatof

which wouldbetheMLEof θ had X1, ...,Xn and Y1, ...,Yn also beenob-
served.

Transcribed Image Text:

On i=1 (X + Y)