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Mean‐squared error estimation in transformed Fay–Herriot models
Author(s) -
Slud Eric V.,
Maiti Tapabrata
Publication year - 2006
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/j.1467-9868.2006.00542.x
Subject(s) - small area estimation , estimator , mean squared error , statistics , estimation , mathematics , best linear unbiased prediction , econometrics , reciprocal , computer science , economics , selection (genetic algorithm) , linguistics , philosophy , management , artificial intelligence
Summary. The problem of accurately estimating the mean‐squared error of small area estimators within a Fay–Herriot normal error model is studied theoretically in the common setting where the model is fitted to a logarithmically transformed response variable. For bias‐corrected empirical best linear unbiased predictor small area point estimators, mean‐squared error formulae and estimators are provided, with biases of smaller order than the reciprocal of the number of small areas. The performance of these mean‐squared error estimators is illustrated by a simulation study and a real data example relating to the county level estimation of child poverty rates in the US Census Bureau's on‐going ‘Small area income and poverty estimation’ project.