Guaranteed Functional Estimation by Samples of Fixed Size: Non-asymptotic Statistical Methods

The classical statistical methods of functional estimation are mainly asymptotic, i.e., the properties of estimators may be investigated only when the sample size unboundedly increases. However, in practice the observation time is always finite, which does not allow one to judge the quality of such estimators. One of the possibilities for finding estimators with the guaranteed quality of statistical inference is provided by the presented truncated estimation method. This method makes it possible to obtain estimators of ratio type functionals by dependent sample on a time interval of a fixed length. Moreover, it is shown that truncated estimators may keep asymptotic properties of basic estimators. As a rule, the truncated estimators represent a mall modification of classical asymptotic estimators. Examples of parametric and non-parametric estimation problems for essentially dependent samples of a fixed size are considered. The presented results can be useful to experts in the field of applied and theoretical statistics.