Schätzern

Schätzern is the German plural term used in statistics for estimators. An estimator, materi­alized by a Schätzer, is a rule or function that produces a numerical estimate of an unknown population parameter from a sample of data. In German-language texts the plural form Schätzern appears in contexts such as “die Schätzern” in dative cases (e.g., den Schätzern).

Purpose and usage

Estimators translate observed data into a best-guess value for a population parameter, such as a mean, proportion, or variance. They are random variables because their outputs depend on the random sample drawn from the population. Estimators are evaluated by properties like bias (whether the average estimate equals the true parameter), variance, and mean squared error. Common goals include unbiasedness, consistency (estimates converge to the true parameter as sample size grows), and efficiency (achieving the lowest possible variance among unbiased estimators, in the sense of the Cramér–Rao bound).

Types and examples

Point estimators provide a single value, such as the sample mean as an estimator of the population mean, or the sample proportion as an estimator of a population proportion. Methods for constructing estimators include maximum likelihood estimation (MLE), method of moments, and Bayesian estimation. The sample variance with the 1/(n−1) normalization is an unbiased estimator of the population variance in many contexts, while the MLE for a normal mean under known variance is the sample mean.

Notation

Estimators are often denoted with a hat, e.g., θ̂ for the estimator of a parameter θ. The term Schätzer is used for the rule itself, and Schätzern refers to the plural form in dative or other cases.

See also: Estimator, Statistical inference, Unbiased estimator, Consistent estimator, Maximum likelihood estimator.