Home Statistical Dictionary Estimator
Estimator
A rule or function that takes sample data and produces a numerical guess for an unknown population parameter -- the general concept underlying every specific technique like the sample mean, maximum likelihood, or OLS.
In Plain English
An estimator is just a recipe: feed it your data, and it hands back a number meant to approximate something you can't observe directly, a population's true mean, a regression coefficient, a variance. The sample mean is an estimator of the population mean; the OLS formula is an estimator of a regression's true slope. "Estimator" is the umbrella word for any such recipe.
Definition
An estimator is a function that maps sample data to a numerical estimate of an unknown population parameter . Because an estimator is a function of random data, it is itself a random variable with its own sampling distribution, and different estimators of the same parameter can be compared on properties like bias, variance, consistency, and efficiency, the central concerns of estimation theory.
Formula
Notation
Properties
- The distinction between an "estimator" (the general rule, a random variable) and an "estimate" (the specific number that rule produces from one particular dataset) is subtle but important -- the same estimator produces a different estimate every time it's applied to a new sample.
- Multiple different estimators can target the same parameter, e.g. both the sample mean and the sample median estimate a symmetric distribution's center, and estimation theory's central task is comparing such competing estimators on properties like bias, variance, and efficiency to determine which is preferable in a given setting.
- An estimator's quality can only be assessed relative to its own sampling distribution, how it would behave across many hypothetical repeated samples, not from the single estimate any one real dataset happens to produce.
At a Glance