PHD-Department of Mathematics

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Robust variance estimation for finite population sampling
(2012-06-08) Otieno, Romanus Odhiambo
After a sample has been obtained the statistic of interest can be computed. The next step (and a ore formidable one) is the assessment of the accuracy (precision) of the resulting statistic. The most commonly used measure of accuracy in the model based survery is the variance of the prediction error associted with teh considered statistic. In general variance are not known and must be estimated using the sampled data. In this thesis we have jproposed new methods for estimating the error variance for finite population sampling. in particular we have considered fixed bandwidth kernel smoothing of the sqared residual and bootstrap technique based on resampling of the rresiduals. Analytical and empirical performances of the new variance estimmators are studied vis avis the robust estimators favoured in teh current practice. On average the proposed estimators have better robustness properties than estimators favored in the current practice. Further more the new estimators have the desired properties of non negativity, simplicity and extend even to cases where some of the current etstimators can not be applied.