Schätzfunktion

A Schätzfunktion, or estimator, is a rule or formula used in statistics to estimate an unknown population parameter based on sample data. A parameter is a numerical characteristic of an entire population, such as the mean or variance. Since it's often impossible or impractical to collect data from the entire population, statisticians use a sample, a subset of the population, to make inferences about the parameter. The Schätzfunktion defines how to use the values from the sample to calculate an estimate for the population parameter.

There are various properties that make a Schätzfunktion desirable. A consistent estimator is one that gets closer to the true population parameter as the sample size increases. An unbiased estimator is one where the expected value of the estimate is equal to the true population parameter. Efficiency refers to how close the estimates are to the true parameter on average; a more efficient estimator has a smaller variance. Common examples of Schätzfunktionen include the sample mean, which estimates the population mean, and the sample variance, which estimates the population variance. The choice of an appropriate Schätzfunktion depends on the specific parameter being estimated and the characteristics of the data.