By Ray Chambers, Robert Clark

This article brings jointly vital principles at the model-based method of pattern survey, which has been built during the last 20 years. appropriate for graduate scholars statisticians, it strikes from uncomplicated rules basic to sampling to extra rigorous mathematical modelling and knowledge research and contains workouts and recommendations.

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**Extra resources for An Introduction to Model-Based Survey Sampling with Applications**

**Example text**

These estimated distributions typically correspond to estimates of proportions (see Chapter 16), and so the above recommendations are directly applicable. In such cases, a compromise allocation somewhere between proportional and optimal allocation is usually employed. 7 How Large a Sample? In the previous two sections we discussed the allocation of the sample between the strata. But what should the total sample size n be under stratiﬁed sampling? g. g. a maximum RSE for the estimate) that are applicable.

8), we know that the prediction variance of the stratiﬁed expansion estimator tˆSy is minimised when h Fh σh is minimised. Substituting σzh for σh , replacing Fh by its approximation, and simplifying leads to h Fh σh ∼ = 1 (dh (ch − ch−1 )) √ (ch − ch−1 ) h 12 39 Deﬁning Stratum Boundaries 1 ∼ = √ 12 1 ∼ =√ 12 2 h h dh (ch − ch−1 ) A2h . So, minimizing the prediction variance is equivalent to minimising h A2h . Note b that h Ah = f (z)dz is equal to a constant, K say, independently of the a choice of Ah .

J). Then starting at the left tail of the histogram, neighbouring classes are joined together to form strata in such a way that each stratum contributes approximately 1/H of the accumulated scores fj . To illustrate this, consider the application of the Dalenius–Hodges method to the Cities’ population, with Z equal to the 1920 population count. We take J = 14, and a class width of 50. 2 below sets out the details of the calculations for the case of H = 2. Note that the method requires the population be ﬁrst ordered by increasing values of Z.