Multiple Frame Surveys. Tracy Xu Kim Williamson Department of Statistical Science Southern Methodist University. Multiple Frame Surveys. Introduction – What is Multiple Frame Survey Different estimators for population total Variance Estimators for those estimators Conclusion
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Department of Statistical Science
Southern Methodist University
– What is Multiple Frame Survey
+ List frame (incomplete, names, addresses)
- Less costly
+ Area frame (complete, insensitive to changes)
- Expensive to sample
+ Can achieve the same precision
C = nAcA + nBcB
+ Using a general population frame as well as std clinics, drug treatment centers, and hospitals
+ Frames: homeless shelters, soup kitchens, and street areas
+ Frames: general population and adult day-care centers
+ How should the information from the
samples be combined to estimate
+ How should variance estimates be
NA= # of elements in Frame A
NB= # of elements in Frame B
Na = # of elements in Frame A, but not Frame B
Nb = # of elements in Frame B, but not Frame A
Nab = # of elements in Frame A & Frame B
and is the smallest root of the quadratic equation
Extensive simulation was done to evaluate the performance of all the estimators in Sharon Lohr and J. N. K Rao(2005) paper
In all the simulations, the PML method had either the smallest EMSE or an EMSE close to the minimum value. With its high efficiency and ease of computation, as well as the practical advantage of using the same set of weights for all response variables, the PML method appears to be a good choice for estimation in multiple frame survey.
When Q>=3, the theoretically optimal Fuller-Burmeister and Hartley methods became unstable, because they require solving systems of equations using a large estimated covariance matrix.
But neither H estimator or PML estimator is necessarily more efficient than the other.
5. The jackknife methods are less stable than the linearization estimator of the variance as judged by the values of relative standard error.
6. For single frame estimator, the jackknife and linearization estimates of the variance coincide.
7. For the other estimators, both the linearization and modified jackknife estimates of the variance are biased downward.