New Models for Seasonal Time Series and a Modification of Akaike’s AIC for Model Multiplicity

Abstract.

The Small Area Income and Poverty Estimation (SAIPE) Program of the Census Bureau produces county-level estimates of child-poverty rates and counts of poor school-aged children, using census, CPS Annual Social and Economic Supplement (ASEC), and administrative-records data, for use in allocation of multi-billion dollar compensatory education allocations. After giving some background on SAIPE and its objectives, and on Small Area Estimation as a statistical topic, the talk will focus on methodological statistical issues in SAIPE small-area estimation, including: (1) SAIPE updates child-poverty estimates derived from the decennial census by using Current Population Survey and administrative-records data, but this creates both an "external" (census) and "internal" (CPS) standard of correctness. These surveys disagree, and the relationship between their estimates changed between 1990 and 2000 (Slud, 2003). (2) Several competing hierarchical or empirical-Bayes models can be used in the estimation: the Fay-Herriot (1979) model treats log CPS counts or rates linearly in (log) predictors with normal errors and variance linear in reciprocal of CPS sample size; while GLMM (random-intercept logistic) models avoid discarding data from sampled counties with no poor children. The fits and small-area estimates are compared via AIC, correlations with census rates, and loss-functions with respect to both truth-standards, using data from the 1990-2000 period. (3) Methods of accurately estimating Mean-Squared Error for Small Area Estimators are well developed in the linear Fay-Herriot model context (Ghosh and Rao 1994, Statist. Sci.). Extensions to the case of nonlinearly transformed Fay-Herriot models are discussed (Slud and Maiti 2004), along with methods to treat the truncation inherent in discarding counties with no sampled poor children