研一四高计真题final2011.pdfVIP

Final:AdvancedEconometricsI

1.(10Points)LetbeasamplemeaninarandomsampleofsizefromaPoisson()

distributionwithpmf()=!,=012.Thefirstmomentandthesecond

momentofPoisson()distributionare()=and(2)=2+.Findthelimiting

distributionof(11)

2.(10Points)Letbei.i.d.withpdf

1

(;)=(+1)(+2)10

Find(1)theumlikelihoodestimatorand(2)themethodofmomentsestimatorof.

3.(15Points)Let1and2betwounbiasedestimatorsofwithvariances2and2,respec-

12

tively.Thevariances2and2donotdependon.Findvaluesandsuchthat

12

(1)Estimator1+2isunbiased.

(2)Unbiasedestimator1+2hasaminimumvarianceif1and2aret.

(3)Unbiasedestimator+hasaminimumvarianceifCov()=,where

121212

11isaconstant.

4.(15Points)Letbearandomsamplefromdistributionwithcdf()=12

1

for1,and0otherwise.Findthelimitingdistribution(cdforpdf)of

(1)();

(2).

(1)

5.(15Points)Assumethat500studentsatacertaincollegewillgraduateonagivenday.

Becauseofspacelimitationsthecollegeofferseachstudenttwoticketsforthecommencement

ceremony.Frompastexperienceitisknownthat50%ofthestudentswillinvitetwoguests

toattendtheceremony,20%studentswillinviteonegu