By Rob J. Hyndman, David M. Bashtannyk and Gary K. Grunwald
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When the sampling variance Vθˆ exists, it would be the limit of the average value of (θˆ i − μθˆ )2 , over i = 1, . . , K, for large K. Extension to the multiparameter case is straightforward. We now distinguish between two common randomization mechanisms that researchers assume to have generated the hypothetical repetitions for determining the distribution of the estimates, and we introduce a third mechanism that can incorporate both. First, for design-based randomization, the sampling distribution for θˆ is based on the probability randomization distribution resulting from the plan for sampling from a ﬁnite population.
Again if the sampling is ignorable, the model variance Vξ [θ] ˆ for Vξp [θ]. 1, to modify the model to incorporate the effect of the sampling mechanism; see, for example, Chambers (1986). An alternative approach that explicitly accounts for the conditional distribution given the sampling mechanism is given in Chapter 39. 3.
In this case, our analysis is primarily descriptive and the population of interest consists of those farmers who engaged in organic farming in 2002 among all the farmers in the ﬁnite population targeted by the survey producer. We see that some differences between the survey population and the target population are due to frame imperfections. 36 D. A. Binder and G. 2. Suppose that we are interested in studying residents of the United States living in households, aged 25–40 years, who were overweight in 1993.