Small area estimation
Encyclopedia
Small area estimation is any of several statistical techniques involving the estimation
of parameter
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 within an area. If a survey has been carried out for the population as a whole (for example, a nation or state-wide survey), the sample size
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
records) that exists for these small areas in order to obtain estimates.
One of the more common small area models
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 country 'i' is
, where 'y' denotes the reported crop area, 
is the regression coefficient, 'x' is the farm-level estimate for either corn or soybean usage from
the satellite data and
represents the county-level effect of any area characteristics that haven't been accounted for.
Estimation
Estimation is the calculated approximation of a result which is usable even if input data may be incomplete or uncertain.In statistics,*estimation theory and estimator, for topics involving inferences about probability distributions...
of parameter
Parameter
Parameter from Ancient Greek παρά also “para” meaning “beside, subsidiary” and μέτρον also “metron” meaning “measure”, can be interpreted in mathematics, logic, linguistics, environmental science and other disciplines....
s for small sub-populations, generally used when the sub-population of interest is included in a larger survey
Statistical survey
Survey methodology is the field that studies surveys, that is, the sample of individuals from a population with a view towards making statistical inferences about the population using the sample. Polls about public opinion, such as political beliefs, are reported in the news media in democracies....
.
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 within an area. If a survey has been carried out for the population as a whole (for example, a nation or state-wide survey), the sample size
Sample size
Sample size determination is the act of choosing the number of observations 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 about a population from a sample...
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
Census
A census is the procedure of systematically acquiring and recording information about the members of a given population. It is a regularly occurring and official count of a particular population. The term is used mostly in connection with national population and housing censuses; other common...
records) that exists for these small areas in order to obtain estimates.
One of the more common small area models
Linear regression
In statistics, linear regression is an approach to modeling the relationship between a scalar variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple regression...
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 country 'i' is
, where 'y' denotes the reported crop area, is the regression coefficient, 'x' is the farm-level estimate for either corn or soybean usage fromthe satellite data and
represents the county-level effect of any area characteristics that haven't been accounted for.