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AgnieszkaZięba,JanKordos
nhc–thesamplesize(numberofindividuals)inthec
thcluster(PSU)ofthehth
stratum.
Inthisworkdifferentlinearizationframeworkwereapplied.Estimation
oftheARPRandRMPGmakesuseofnonparametrictechniquesofquantile
estimation.Theasymptoticvariancesoftheseestimatorsinvolvethedensity(f)
oftheunderlyingprobabilitydistributionandstandardkernelestimatorswere
applied.EstimationofS80/S20iscloselyrelatedtothetheoryofM-estimators
andGINIcanbeestimatedbyaU-statistic[Niemiro,Wieczorkowki,2005].
MEAN_EQINCislinearfunctionandinthiscaseclassicalapproachfortotal
valuedividedbysumofweightscanbeapplied.
4.Theresamplingmethods
Thelinearizationmethodofapproximatingvarianceofcomplex(non-
linear)statisticsisalong-establishedprocedurewhereasresamplingapproach
isbyfarthesimplesttechnically[Betti,Verma,2005].
Thejackknifeandbootstrapmethodsarewidelyusedinsamplesurveys
[Shao,Tu,1995].Thesemethodsbasedonrepeatedlyresamplingtheoriginal
dataandenableinferencefromcreatedresamples.Itisanalternativefor
linearizationmethodsortraditionalapproachinwhichaccuracymeasureis
estimatedbyanempiricalanalogyoftheoreticalformulaofaccuracymeasure
(oritsapproximation)basedonpostulatedmodel[Shao,Tu,1995].Inpractice
theresamplingmethodsdonotneedtheoreticalformula.Thismakesstatistical
inferencemorestraightforwardbutalsowithlargeamountofcomputation.
5.Thejackknife
Thejackknifemethodwasinventedin1956byQuenouilleand
developedfurtherbyTukeyin1957[Betti,Verma,2005].Supposeasample
X
1
,
X
2
,...,
X
n
istobeusedtoestimateapopulationparameter
θ
.Thebasic
jackknifeprocedureistodeleteoneobservation
j
=
1
,
2
,...,
n
intheoriginal
sample
X
1
,
X
2
,...,
X
n
andcomputeestimate
θ
ˆ
−
j
usingreduceddata.This
procedureisrepeatedntimes.Thedistributionofthe
θ
ˆ’sisrelatedtothe
−
j
distributionof
θ
ˆ.Thevariabilityof
θ
ˆabout
θ
canbeassessedbythe
variabilityof
θ
ˆ
−
j
about
θ
ˆ.
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