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Benchmarked Estimators for a Small Area Mean Under a Onefold Nested Regression Model
Author(s) -
Stefan Marius,
Hidiroglou Michael
Publication year - 2021
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/insr.12380
Subject(s) - estimator , extremum estimator , mathematics , small area estimation , m estimator , statistics , mean squared error , benchmarking , population , regression , variable (mathematics) , regression analysis , mathematical analysis , demography , marketing , sociology , business
Summary In this paper, we modify small area estimators, based on the unit‐level model, so that they add up to reliable higher‐level estimates of population totals. These modifications result in benchmarked small area estimators. We consider two benchmarking procedures. One is based on augmenting the unit‐level model with a suitable variable. The other one uses the calibrated weights of the direct estimators that are reliable at the higher levels. These weights are used in estimators that are based on the aggregation of the unit‐level model for each small area. The mean squared error estimators of the proposed benchmarked estimators are obtained by suitably modifying those associated with the corresponding non benchmarked estimators. The properties of the estimators are evaluated via simulation.