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Confidence intervals for estimators of welfare indices under complex sampling
Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2010.
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| Format: | Thesis |
| Language: | English |
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Stellenbosch : University of Stellenbosch
2010
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| _version_ | 1867613772464521216 |
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| access_status_str | Open Access |
| author | Kirchoff, Retha |
| author2 | De Wet, Tertius |
| author_browse | De Wet, Tertius Kirchoff, Retha |
| author_facet | De Wet, Tertius Kirchoff, Retha |
| author_sort | Kirchoff, Retha |
| collection | Thesis |
| dc_rights_str_mv | University of Stellenbosch |
| description | Thesis (MComm (Statistics and Actuarial Science))--University of Stellenbosch, 2010. |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/4351 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:41:26.849Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2010 |
| publishDateRange | 2010 |
| publishDateSort | 2010 |
| publisher | Stellenbosch : University of Stellenbosch |
| publisherStr | Stellenbosch : University of Stellenbosch |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/4351 Confidence intervals for estimators of welfare indices under complex sampling Kirchoff, Retha De Wet, Tertius Neethling, Ariane University of Stellenbosch. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science. Sampling Dissertations -- Statistics and actuarial science Theses -- Statistics and actuarial science Assignments -- Statistics and actuarial science Welfare indices Confidence intervals Welfare indices -- Estimation 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. Masters 2010-03-01 2010-03-01 2010-03 Thesis http://hdl.handle.net/10019.1/4351 en University of Stellenbosch 188 p. application/pdf Stellenbosch : University of Stellenbosch |
| spellingShingle | Sampling Dissertations -- Statistics and actuarial science Theses -- Statistics and actuarial science Assignments -- Statistics and actuarial science Welfare indices Confidence intervals Welfare indices -- Estimation Kirchoff, Retha Confidence intervals for estimators of welfare indices under complex sampling |
| title | Confidence intervals for estimators of welfare indices under complex sampling |
| title_full | Confidence intervals for estimators of welfare indices under complex sampling |
| title_fullStr | Confidence intervals for estimators of welfare indices under complex sampling |
| title_full_unstemmed | Confidence intervals for estimators of welfare indices under complex sampling |
| title_short | Confidence intervals for estimators of welfare indices under complex sampling |
| title_sort | confidence intervals for estimators of welfare indices under complex sampling |
| topic | Sampling Dissertations -- Statistics and actuarial science Theses -- Statistics and actuarial science Assignments -- Statistics and actuarial science Welfare indices Confidence intervals Welfare indices -- Estimation |
| url | http://hdl.handle.net/10019.1/4351 |
| work_keys_str_mv | AT kirchoffretha confidenceintervalsforestimatorsofwelfareindicesundercomplexsampling |