Minimax estimation of a cumulative distribution function by converting to a parametric problem |
| |
Authors: | Alicja Jokiel-Rokita Ryszard Magiera |
| |
Affiliation: | (1) Institute of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, 50-370, Poland |
| |
Abstract: | Let X = (X 1,...,X n ) be a sample from an unknown cumulative distribution function F defined on the real line . The problem of estimating the cumulative distribution function F is considered using a decision theoretic approach. No assumptions are imposed on the unknown function F. A general method of finding a minimax estimator d(t;X) of F under the loss function of a general form is presented. The method of solution is based on converting the nonparametric problem of searching for minimax estimators of a distribution function to the parametric problem of searching for minimax estimators of the probability of success for a binomial distribution. The solution uses also the completeness property of the class of monotone decision procedures in a monotone decision problem. Some special cases of the underlying problem are considered in the situation when the loss function in the nonparametric problem is defined by a weighted squared, LINEX or a weighted absolute error. |
| |
Keywords: | Nonparametric estimation Minimax estimation Cumulative distribution function Binomial distribution Loss function |
本文献已被 SpringerLink 等数据库收录! |