DemnatiRao (2004) linearization variance estimator in two-phase sampling. The linearization variance estimator presented in Exercise 23 of
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Demnati–Rao (2004) linearization variance estimator in two-phase sampling. The linearization variance estimator presented in Exercise 23 of Chapter 9 can be extended to two-phase sampling. Let θ be the population quantity of interest, and define the estimator ˆθ to be a function of the vectors of sampling weights for the phase I and phase II samples and the population values:
And
Then,
- Consider the two-phase ratio estimator in (12.9).We can write
Where wi = w (1)i w(2)i . Show that the Demnati-Rao linearization variance estimator is
- Suppose that the phase I sample is an SRS of size n (1) and the phase II sample is an SRS of size n (2). What is ˆVDR (ṫ (2) yr) for this case?
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