Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2010. / ENGLISH ABSTRACT: The aim of this study is to obtain estimates and confidence intervals for welfare
indices under complex sampling. It begins by looking at sampling in general with
specific focus on complex sampling and weighting. For the estimation of the welfare
indices, two resampling techniques, viz. jackknife and bootstrap, are discussed.
They are used for the estimation of bias and standard error under simple random
sampling and complex sampling. Three con dence intervals are discussed, viz. standard
(asymptotic), percentile and bootstrap-t. An overview of welfare indices and
their estimation is given. The indices are categorized into measures of poverty and
measures of inequality. Two Laeken indices, viz. at-risk-of-poverty and quintile
share ratio, are included in the discussion. The study considers two poverty lines,
namely an absolute poverty line based on percy (ratio of total household income
to household size) and a relative poverty line based on equivalized income (ratio of
total household income to equivalized household size). The data set used as surrogate
population for the study is the Income and Expenditure survey 2005/2006
conducted by Statistics South Africa and details of it are provided and discussed.
An analysis of simulation data from the surrogate population was carried out using
techniques mentioned above and the results were graphed, tabulated and discussed.
Two issues were considered, namely whether the design of the survey should be considered
and whether resampling techniques provide reliable results, especially for
con dence intervals. The results were a mixed bag . Overall, however, it was found
that weighting showed promise in many cases, especially in the improvement of the
coverage probabilities of the con dence intervals. It was also found that the bootstrap
resampling technique was reliable (by looking at standard errors). Further
research options are mentioned as possible solutions towards the mixed results. / AFRIKAANSE OPSOMMING: Die doel van die studie is die verkryging van beramings en vertrouensintervalle vir
welvaartsmaatstawwe onder komplekse steekproefneming. 'n Algemene bespreking
van steekproefneming word gedoen waar daar spesi ek op komplekse steekproefneming
en weging gefokus word. Twee hersteekproefnemingstegnieke, nl. uitsnit
(jackknife)- en skoenlushersteekproefneming, word bespreek as metodes vir die beraming
van die maatstawwe. Hierdie maatstawwe word gebruik vir sydigheidsberaming
asook die beraming van standaardfoute in eenvoudige ewekansige steekproefneming
asook komplekse steekproefneming. Drie vertrouensintervalle word bespreek, nl.
die standaard (asimptotiese), die persentiel en die bootstrap-t vertrouensintervalle.
Daar is ook 'n oorsigtelike bespreking oor welvaartsmaatstawwe en die beraming
daarvan. Hierdie welvaartsmaatstawwe vorm twee kategorieë, nl. maatstawwe van
armoede en maatstawwe van ongelykheid. Ook ingesluit by hierdie bespreking is die
at-risk-of-poverty en quintile share ratio wat deel vorm van die Laekenindekse.
Twee armoedemaatlyne , 'n absolute- en relatiewemaatlyn, word in hierdie studie
gebruik. Die absolute armoedemaatlyn word gebaseer op percy , die verhouding van
die totale huishoudingsinkomste tot die grootte van die huishouding, terwyl die relatiewe
armoedemaatlyn gebasseer word op equivalized income , die verhouding van
die totale huishoudingsinkomste tot die equivalized grootte van die huishouding.
Die datastel wat as surrogaat populasie gedien het in hierdie studie is die Inkomste
en Uitgawe opname van 2005/2006 wat deur Statistiek Suid-Afrika uitgevoer is. Inligting
met betrekking tot hierdie opname word ook gegee. Gesimuleerde data vanuit
die surrogaat populasie is geanaliseer deur middel van die hersteekproefnemingstegnieke
wat genoem is. Die resultate van die simulasie is deur middel van gra eke en
tabelle aangedui en bespreek. Vanuit die simulasie het twee vrae opgeduik, nl. of
die ontwerp van 'n steekproef, dus weging, in ag geneem behoort te word en of die
hersteekproefnemingstegnieke betroubare resultate lewer, veral in die geval van die vertrouensintervalle. Die resultate wat verkry is, het baie gevarieer. Daar is egter
bepaal dat weging in die algemeen belowende resultate opgelewer het vir baie van die
gevalle, maar nie vir almal nie. Dit het veral die dekkingswaarskynlikhede van die
vertrouensintervalle verbeter. Daar is ook bepaal, deur na die standaardfoute van
die skoenlusberamers te kyk, dat die skoenlustegniek betroubare resultate gelewer
het. Verdere navorsingsmoontlikhede is genoem as potensiële verbeteringe op die
gemengde resultate wat verkry is.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/4351 |
| Date | 03 1900 |
| Creators | Kirchoff, Retha |
| Contributors | De Wet, T., Neethling, A., University of Stellenbosch. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science. |
| Publisher | Stellenbosch : University of Stellenbosch |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | Unknown |
| Type | Thesis |
| Format | 188 p. |
| Rights | University of Stellenbosch |
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