Small area estimation is any of several

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

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 der ...

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-population In statistics, a population is a set of similar items or events which is of interest for some question or experiment. A statistical population can be a group of existing objects (e.g. the set of all stars within the Milky Way galaxy) or a hypo ...

s, generally used when the sub-population of interest is included in a larger

survey Survey may refer to: Statistics and human research * Statistical survey, a method for collecting quantitative information about items in a population * Survey (human research), including opinion polls Spatial measurement * Surveying, the techniq ...

. 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 statistical study of populations, especially human beings. Demographic analysis examines and measures the dimensions and dynamics of populations; it can cover whole societies or groups defined by criteria such as edu ...

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 is the act of choosing the number of observations or Replication (statistics), 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 stat ...

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 is the procedure of systematically acquiring, recording and calculating information about the members of a given population. This term is used mostly in connection with national population and housing censuses; other common censuses incl ...

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 ''modulus'', a measure. Models c ...

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