Generalized variance functions, mall area estimation, poverty rates
In areas with small sample size, the estimates of sampling variability of rate estimates can have high uncertainty. Treating these estimated variances as the true sampling error variances in models for the underlying true rate can increase the mean squared error (Bell 2008). In counties with small sample sizes, the variance estimates of poverty statistics from the American Community Survey show wide variation even after accounting for sample size. Generalized Variance Functions (GVF) can be used to smooth out the uncertainty of the design-based variance estimates. We propose incorporating GVFs with small area model techniques to improve the variability of variance estimates in counties where the precision of the design-based variance is lacking. These smoothed variances can then be used in small area models for poverty rate estimates.
Jerry J. Maples. (2011). Using Small Area Modeling to Improve Design-Based Estimates of Variance for County Level Poverty Rate Estimates in the American Community Survey. Center for Statistical Research & Methodology, Research and Methodology Directorate Research Report Series (Statistics #2011-02). U.S. Census Bureau. Available online at <http://www.census.gov/srd/papers/pdf/rrs2011-02.pdf>.
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