Browsing by Author "Kirchoff, Retha"

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    Confidence intervals for estimators of welfare indices under complex sampling
    (Stellenbosch : University of Stellenbosch, 2010-03) Kirchoff, Retha; De Wet, Tertius; Neethling, Ariane; University of Stellenbosch. Faculty of Economic and Management Sciences. Dept. of Statistics and Actuarial Science.
    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.