Small area estimation is any of several

statistical Statistics (from German language, German: ', "description of a State (polity), state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a s ...

techniques involving the

estimation Estimation (or estimating) is the process of finding an estimate or approximation, which is a value that is usable for some purpose even if input data may be incomplete, uncertain, or unstable. The value is nonetheless usable because it is d ...

parameter A parameter (), generally, is any characteristic that can help in defining or classifying a particular system (meaning an event, project, object, situation, etc.). That is, a parameter is an element of a system that is useful, or critical, when ...

s for small sub-populations, generally used when the sub-population of interest is included in a larger survey. 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

demographic Demography () is the statistics, statistical study of human populations: their size, composition (e.g., ethnic group, age), and how they change through the interplay of fertility (births), mortality (deaths), and migration. Demographic analy ...

within an area. If a survey has been carried out for the population as a whole (for example, a nation or statewide survey), the

sample size Sample size determination or estimation is the act of choosing the number of observations or replicates to include in a statistical sample. The sample size is an important feature of any empirical study in which the goal is to make inferences abo ...

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

census A census (from Latin ''censere'', 'to assess') is the procedure of systematically acquiring, recording, and calculating population information about the members of a given Statistical population, population, usually displayed in the form of stati ...

records) that exists for these small areas in order to obtain estimates. One of the more common small area

models A model is an informative representation of an object, person, or system. The term originally denoted the plans of a building in late 16th-century English, and derived via French and Italian ultimately from Latin , . Models can be divided int ...

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. The final model resulting from this for unit/farm 'j' in county 'i' is

y_ = x_'\beta +\mu_i +\epsilon_  \,

, where 'y' denotes the reported crop area,

\beta \,

is the regression coefficient, 'x' is the farm-level estimate for either corn or soybean usage from the satellite data and

\mu \,

represents the county-level effect of any area characteristics unaccounted for. The Fay-Herriot model, 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.

Further reading