tailieunhanh - Analysis of Survey Data phần 6

Khi các đường thẳng đứng được rút ra từ chỉ số BMI Â 20 sau đó DBMI Â 20 là ở đuôi trên của phân phối. Tại BMI Â 28 hoặc 29, đầu phía trên của âm mưu đường viền giảm xuống dưới DBMI Â 28. Điều này cho thấy rằng phụ nữ thường muốn cân nhắc cho bất kỳ trọng lượng nhất định. Nó cũng cho thấy rằng mong muốn giảm cân trung bình tăng | INFERENCE UNDER INFORMATIVE PROBABILITY SAMPLING 179 The sample distribution is different also from the familiar pX distribution defined as the combined distribution over all possible realizations of the finite population measurements the population X distribution and all possible sample values for a given population the randomization p distribution . The pX distribution is often used for comparing the performance of design-based estimators in situations where direct comparisons of randomization variances or mean square errors are not feasible. The obvious difference between the sample distribution and the pX distribution is that the former conditions on the selected sample and values of auxiliary variables measured for units in the sample whereas the latter accounts for all possible sample selections. Finally rather than conditioning on the selected sample when constructing the sample distribution and hence the sample likelihood one could compute instead the joint distribution of the selected sample and the corresponding sample measurements. Denote by ys yt t 2 s the outcome variable values measured for the sample units and by xs xt t 2 s and xs xt t 2 s the values of the auxiliary variables corresponding to the sampled and nonsampled units. Assuming independence of the population measurements and independent sampling of the population units Poisson sampling the joint pdf of s ys xs xs can be written as f s ys xs xs p yt xỉ fu yt xz p xt p xt 1 - p xt where p yt xt EU p yt xt and p xt EU p xt . Note that the product of the terms in the first set of square brackets on the right hand side of is the joint sample pdf fs ys xs s for units in the sample as obtained from . The use of for likelihood-based inference has the theoretical advantage of employing the information on the sample selection probabilities for units outside the sample but it requires knowledge of the expectations p xt EU p xt for all t 2 U and hence the values xs. This information

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