small area estimation - small area methods for

SmallAreaEstimation1-Smallareaestimation problem2- Estimation fordomains - Directestimators –

estimation forplanned domains3– Coefficient ofVariation andMinimumlevel of

precision4- Estimation forunplanned domains and/or

where thesamplesize is not enough fortheminimumlevel ofprecision – Indirect estimators

Recap

• Targetparameters inthedomain:

• Totalofthestudy variable• Mean ofthestudy variable• Atrisk ofpoverty rate• Poverty gap

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FromStatisticsCanada (2010).Guide totheLabour ForceSurveySAEmethods:

StatisticsCanadaapplies thefollowingguidelinesonLFSdatareliability:-ifCV≤16.5%thendirectestimates aredisseminatedwithout restrictions (norelease)-if16.5%<CV≤33%thentheestimates shouldbeaccompaniedbywarning(releasewithcaveat)-ifCV>33%thentheestimatesarenotrecommended foruse(norelease)

These thresholdmaybegoodforlabour marketvariables.

Whendirectestimatesarenotreliable?

WhatifwearedealingwithestimateswithCV>33%?

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Ifadomainsamplecannotsupportdirectestimatesofadequateprecision,oftenindirectestimateisusedto“borrowstrength”byusingvaluesfromrelatedareasand/ortimeperiodstoincreaseeffectivesamplesize.

Thesevaluesareusedintheestimationthroughamodel(implicitlyorexplicitly)thatprovidesalinktorelatedareasand/ortimeperiodsthroughsupplementaryinformationsuchasrecentcensuscountsorcurrentadministrativerecordsrelatedtothevariableofinterest.

Not direct DomainEstimates – Indirect estimates

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Itispossibletodividetheindirectestimatesinto:

— DomainIndirect:usesvaluesfromanotherdomainbutnotfromanothertime.— TimeIndirect:usesvaluesfromanothertimebutnotfromanotherdomain.— DomainandTimeIndirect:usesvaluesbothfromanotherdomainandtime.

Indirect Domain Estimates

SAE: Borrowing Strength from?

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Wecandistinguishtheindirectmethods into:

— SyntheticEstimator: anestimator iscalledasyntheticestimator ifareliabledirectestimator foralargearea, coveringseveral smallareas, isusedtoderiveanindirectestimator forasmallareaunder theassumption thatthesmallareashavethesamecharacteristics asthelargearea.Asaconsequence, thevarianceofasyntheticestimator islowerthanthecorresponding directestimatorbutisbiasedifthemodelassumptions arenotsatisfied.— Composite Estimator: itisalinearcombinationbetween adirectestimatorandasyntheticestimator.Forthisreason itrepresents agoodcompromise intermsofefficiencybetween thecharacteristics ofthetwocomponents.

Indirect Domain Estimates

Synthetic estimator

Synthetic estimator

Broad AreaRatioEstimator(BARE)

Synthetic estimator

Broad AreaRatioEstimator(BARE)withauxiliary data

Ratioestimator, Regression estimator

Compositeestimator

:HTestimator orsimple ratioestimator

:regression estimator

Thechoice oftheweight

Comparison Between Direct,SyntheticandCompositeEstimator

Empirical comparison of small area estimation methods for the Italian Labor Force Survey (LFS)

• Performance of small area estimators are studied by simulating sample selection from 1981 Population Census.

• Samples are 400samplereplicates (h),each ofidentical sizeoftheLFSsampledrawn following the LFS design (two stages with stratication)

• Design-based properties of the estimators: verification of itsBias and calculation of the CV of the estimator

Tzavidis,Salvati,Marchetti(MOOC2020)


Empirical comparison of small area estimation methods for the Italian Labor Force Survey (LFS)

• Activepopulation,aged 15-64- annual averages - According tothedefinitions ofthe InternationalLabour Organisation (ILO)forthepurposes ofthelabour marketstatistics people areclassified as employed,unemployed andeconomicallyinactive.Theeconomically active population is thesumofemployed andunemployed persons.Inactive persons arethose who,during thereference week,were neither employed nor unemployed.

• Example - 14Health ServiceAreas (HSA)oftheFriuliVeneziaGiuliaRegion areconsidered tobesmallareas

• Yi – true mean ofthey variable inthedomain i (HSA)– annual average ofactivepopulation (known fromtheCensus)

Tzavidis,Salvati,Marchetti(MOOC2020)

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Furtherwehave,dependingonthe“reference framework” forinference:

— DesignBasedApproach: Estimatorproperties areassessed withrespecttothesamplingdesign(see previousexample).Thisframework isusedforsmallareaestimation,mainlybecauseofitssimplicity.

—ModelAssistedApproach: Inpractice, thevaluesofYaretypicallydefinedbyassumingamodelforthedistributionofYgivenX.Thatis,practitionershavebeenwillingtousemodels inordertoidentifyoptimalstrategies forestimatingTY.However, theirassessment ofthesestrategies remaindesign-based (Särndal,Swensson andWretman,1992).

— ModelBasedApproach:design-unbiasedness isnolongerarequirement,thealternative propertywerequireoftheestimatorunder thisapproachisthatitbemodel-unbiased giventhesampleSandauxinfoX.

Inference framework

Undirect estimation

Synthetic estimator(BARE,ratio,regression)

Composite estimator

Calibration estimators GREG

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Model Based Approach

Twotypesofmodels depending onthedata:arealevel modelandunit level model.

— AreaLevelModel:arealevelmodelsareappropriate ifonlyarea-levelsummarydataavailablefortheauxiliaryand/ortheresponse variables. Itispossible totakeintoaccountthesamplingweights intomodel.

— UnitLevelModel:unitlevelmodels aregenerallytopreferifunit-specificinformation isavailable.Theyusually ignorethesurveyweights.

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Auxiliary information in Area Level Approach

Whenonlysummarydata(suchasthetraditional surveyestimator) fortheresponsevariable isavailableatthesmallarealevel:

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Auxiliary information in Unit Level Approach

Whendataforboththeresponse variableandauxiliaryvariablesareavailableattheunit level:

• Examples ofapplication oftheSynthetic andcompositeestimatorduring theR lab

small area estimation - small area methods for

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