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in use today is the 'nested area unit level regression model', first used in 1988 to model corn and soybean crop areas in Iowa. The initial survey data, in which farmers reported the area they had growing either corn or soybeans, was compared to estimates obtained from satellite mapping of the farms.
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within any particular small area may be too small to generate accurate estimates from the data. To deal with this problem, it may be possible to use additional data (such as
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The term "small area" in this context generally refers to a small geographical area such as a county. It may also refer to a "small domain", i.e. a particular
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Jiang, J., and Lahiri, P. "Mixed model prediction and small area estimation", Editor's invited discussion paper, "Test," Vol. 15, 1, (2006), 1-96.
196:, a random effects model, has been used to make estimates for small domains when the sample from each domain is too small for fixed effects.
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within an area. If a survey has been carried out for the population as a whole (for example, a nation or statewide survey), the
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is the regression coefficient, 'x' is the farm-level estimate for either corn or soybean usage from the satellite data and
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213:. "An error component model for prediction of county crop areas using survey and satellite data",
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Statistical techniques involving the estimation of parameters for small sub-populations
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represents the county-level effect of any area characteristics unaccounted for.
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Danny
Pfefferman. "Small area estimation – New developments and directions",
38:, generally used when the sub-population of interest is included in a larger
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records) that exists for these small areas in order to obtain estimates.
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The final model resulting from this for unit/farm 'j' in county 'i' is
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M. Ghosh, J. N. K. Rao. "Small area estimation: An appraisal",
140:{\displaystyle y_{ij}=x_{ij}'\beta +\mu _{i}+\epsilon _{ij}\,}
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215:Journal of the American Statistical Association
229:http://projecteuclid.org/euclid.ss/1177010647
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238:International Statistical Review
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26:techniques involving the
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245:Small area estimation
243:J. N. K. Rao (2003),
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