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Content: The first part of the course gives the basic foundations of design based inference when sampling from finite populations. Concepts, such as sampling design, inclusion probabilities, the sample membership indicators, (design)expectations, (design)variance and (design)covariance are introduced. The Horvitz-Thompson estimator for a population total is introduced and discussed. The general results are applied to several sampling designs, often used in practice. Moreover, estimation of ratios and medians are discussed. In the second part of the course the difference estimator and regression estimator are introduced for an arbitrary sampling design. These estimators incorporate auxiliary information explicitly, with a view to achieving more efficient estimations. The general results are applied to some often used element sampling designs. The third part of the course gives an introduction to estimation of domains (subpopulations) as well as the theory of two-phase sampling and its applications to certain problems of non-response. |
