schätzer

Schätzer is a German noun meaning a person who estimates or values something. In a statistical context, the term Schätzer refers to a rule, function, or procedure that produces an estimate of an unknown quantity based on observed data. A Schätzer may be a Punktschätzer (point estimator), which yields a single value, or an Intervallschätzer (interval estimator), which provides an interval that is believed to contain the parameter with a specified confidence level.

Key concepts associated with Schätzer include bias, variance, consistency and efficiency. Bias measures systematic error, with an unbiased Schätzer having an expected value equal to the parameter. Variance reflects precision; lower variance is generally desirable. Consistency means that the Schätzer converges in probability to the true parameter as the sample size grows. Efficiency compares variances among competing Schätzers, with more efficient estimators having smaller variance for the same parameter.

Common examples are the sample mean as a Schätzer of the population mean and the sample variance as a Schätzer of the population variance (with the appropriate normalization). Popular classes of Schätzers include the Maximum Likelihood Schätzer (MLE-Schätzer) and various least-squares Schätzers.

Etymology and usage: the word derives from schätzen (to estimate or value) with the agent suffix -er. Schätzer also exists as a surname in German-speaking regions.

See also: estimation, Schätzung, Punktschätzer, Intervallschätzer.