Properties of estimators

Especially in the following chapters, designations such as bias or asymptotic unbiasedness will be used repeatedly. These expressions are used to describe properties of an estimator. These terms are explained briefly here.

Assumption: The distribution of the sample elements has an unknown parameter . A function t that approximately estimates from the sample values the parameter is given by:

Generally a function of a sample, is noted as statistics. In the case of estimation of parameters, we talk about a function for estimation, short estimator t. The realization of an estimator, such as is called estimation.

Depending on the sample obtained, other results for the point estimate are gained. For example, if 1,000 people are asked about their income by drawing 1,000 people from a finite population, the mean income would differ when another 1,000 people are drawn. Practically speaking, performed point estimates are therefore only useful when the accuracy of the results...