By Ray Chambers, Robert Clark
This article brings jointly very important principles at the model-based method of pattern survey, which has been built over the past 20 years. appropriate for graduate scholars statisticians, it strikes from easy rules primary to sampling to extra rigorous mathematical modelling and information research and contains routines and recommendations.
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Extra info for An Introduction to Model-Based Survey Sampling with Applications
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. 2), the BLUP is also an EB predictor. To deﬁne the BLUP, we will ﬁrst deﬁne linear predictors to be those that can be written as a linear combination of the values of Y associated with sample units. Linear predictors are used extensively in survey sampling, mainly because of ty under a speciﬁed model satisﬁes of their simplicity of use.
1, with stratum h = 1 containing the cities with the largest 1920 population counts, and stratum h = 2 containing the remainder. 2. Randomly allocate 16 of the 64 cities to stratum 1 and the remaining 48 to stratum 2. 1. Call this random stratiﬁcation. Let Uh denote summation over all the population units in stratum h. 1). The strata variance parameters σh2 are approximately equal to 2 σ ˆh2 = Syh = (Nh − 1)−1 Uh (yi − y¯h )2 where y¯h denotes the average value of Y in stratum h. 2 2 Under size stratiﬁcation, Sy1 = 53, 843, while Sy2 = 5, 581.
2) Here h indexes the strata, Nh is the stratum population size, nh is the stratum sample size and y¯sh is the sample mean of Y in stratum h. 2) above is usually called the stratiﬁed expansion estimator. 1). 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.
An Introduction to Model-Based Survey Sampling with Applications by Ray Chambers, Robert Clark