Geometrical aspects of testing complex statistical hypotheses in mathematical simulation

Statistical Testing of Hypotheses

Geometrical aspects of statistical learning theory

Geometry plays an important role in modern statistical learning theory, and many different aspects of geometry can be found in this fast developing field. This thesis addresses some of these aspects. A large part of this work will be concerned with so called manifold methods, which have recently attracted a lot of interest. The key point is that for a lot of real-world data sets it is natural t...

Testing Statistical Hypotheses in Fuzzy Environment

In traditional statistics all parameters of the mathematical model and possible observations should be well defined. Sometimes such assumption appears too rigid for the real-life problems, especially while dealing with linguistic data or imprecise requirements. To relax this rigidity fuzzy methods are incorporated into statistics. We review hitherto existing achievements in testing statistical ...

TESTING STATISTICAL HYPOTHESES UNDER FUZZY DATA AND BASED ON A NEW SIGNED DISTANCE

This paper deals with the problem of testing statisticalhypotheses when the available data are fuzzy. In this approach, wefirst obtain a fuzzy test statistic based on fuzzy data, and then,based on a new signed distance between fuzzy numbers, we introducea new decision rule to accept/reject the hypothesis of interest.The proposed approach is investigated for two cases: the casewithout nuisance p...

Testing fuzzy hypotheses with vague data

The problem of testing fuzzy hypotheses in the presence of vague data is considered. A new method based on the necessity index of strict dominance (NSD) is suggested. An example hoe to apply the proposed test in statistical quality control is shown.