Get An Introduction to Model-Based Survey Sampling with PDF

By Ray Chambers, Robert Clark

ISBN-10: 019856662X

ISBN-13: 9780198566625

This article brings jointly very important rules at the model-based method of pattern survey, which has been built during the last two decades. compatible for graduate scholars statisticians, it strikes from simple rules basic to sampling to extra rigorous mathematical modelling and information research and contains routines and strategies.

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2) above is commonly called the expansion estimator. Note that the EB predictor is not necessarily unique, as there may be several possible estimators of unknown parameters such as μ. However, it provides a simple way to construct predictors, and will be statistically efficient if a sensible method of parameter estimation is used. An alternative, more complex approach, called Best Linear Unbiased Prediction, can also be used. This method does yield a unique best predictor, called the Best Linear Unbiased Predictor, or BLUP.

1c). Note that if some strata are not represented in the sample, then it is not possible to use the stratified expansion estimator, since y¯sh will not be defined for those strata. In this case, there is no unbiased estimator of ty . Ideally, we should select our sample in such a way that every stratum is represented, so that this problem does not arise. 5) with the addition of a stratum subscript, that is Var tˆSy − ty = h Var tˆE yh − tyh = h Nh2 /nh (1 − nh /Nh )σh2 . 3) is straightforward. 6)) to get Vˆ tˆSy = h Vˆ tˆE yh = h Nh2 /nh (1 − nh /Nh )s2yh .

1 The Homogeneous Strata Population Model A model for a stratified population follows naturally from our definition of strata as made up of population elements that are homogeneous with respect to other elements of the same stratum and heterogeneous with respect to elements of other strata. We will use the following model for the distribution of population Y -values across strata h = 1, . , H: E(yi |i ∈ h) = μh Var (yi |i ∈ h) = σh2 yi and yj are independent when i = j. 1c) 30 Stratified Populations Here i ∈ h indicates that population unit i is in stratum h.

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An Introduction to Model-Based Survey Sampling with Applications by Ray Chambers, Robert Clark

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