Neural networks are among those mathematical models which are used to model non-linear time series with high accuracy. The advantage with these linear times series as opposed to topical ones is that they don’t require restrictive assumptions. The accuracy of neural network based estimators as nonparametric models is of high importance. In that light, we can use BOOTSTRAPping to calculate the accuracy of estimators in the time series’ complex nonlinear structures. Though introduced in recent years these methods yield more accurate results in the bias calculation of estimators compared to the other ones. This paper introduces neural network BOOTSTRAP, BOOTSTRAP AUTOregressive, moving block BOOTSTRAP method and residual BOOTSTRAP methods in time. Then these four algorithms are compared with each other in a simulation study. Finally an example related to Iran’s kerosene price monthly data is worked out.

Efron's BOOTSTRAP method can only be used to estimate the precision measures of estimators when observations are independent. For spatial data that are spatially correlated, the moving block BOOTSTRAP method is usually used. But, in this method, the boundary observations have less chance of presence in blocks resampling than the other observations. In this paper, the new separate block BOOTSTRAP method is introduced and an algorithm is given for estimating the precision measures of estimators. A simulation study is carried out to compare the efficiency of the separate block BOOTSTRAP method with moving block BOOTSTRAP. It is shown that, with their method we can estimate the bias of sample mean with no error, and the estimator for variance of sample mean is consistent.

This paper introduces the concept of AUTO–Engel polygroups via the heart of hypergroups and investigates the relation between of AUTO–Engel polygroups and AUTO–nilpotent polygroups. Indeed, we show that the concept of heart of hypergroups plays an important role on construction of AUTO–Engel polygroups. This study considers the notation of characteristic set in hypergroups with respect to AUTOmorphism of hypergroups and shows that the heart of hypergroups is a characteristic set in hypergroups.

Some of DMUs that are evaluated as efficient units by DEA, have performance score one, so, in terms of theory, they are not distinction between them. Since, decision makers want to better assess DMUs performance and further improve the process, some of them try to full rank theirs. There are different methods for ranking efficient and inefficient units and many papers have been published in this field that they have many faults and they cannot rank all DMUs. BOOTSTRAPping method, proposed in this article, can rank all DMUs. Boot strapping process uses the theory of computing power and linear programming is used for performance scores BOOTSTRAP and hence, it has not problems of the previous methods.