Systemische Resilienz – Die Perspektiven und das Resilienz-Quadarat

In the article results of resilience research are presented and a systemic concept of resilience is derived, which differentiates the term from other models regarding psychic health. The resilience square shows essential factors for resilience. Based on this the idea of resilience is transferred to systems and organizations. The article deepens the resilience approach of Mohr (2016).     

Modified minimax estimation of regression coefficients

Working with the linear regression model (1.1) and having the extraneous information (1.2) about regression coefficients the problem exists how to build estimators (1.3) with the risk (1.4) which enable to utilize the known information in order to reduce their risk as compared with the risk (1.6) of the LSE (1.5). Solution of this problem is known for the positive definite matrix T, namely in form for estimators (1.8) and (1.10).First, it is shown that the proposed estimators (2.6),(2.9) and (2.16) based on psedoinversions of the matrix L represent the solution of the problem of the positive semidefinite matrix T=L'L.Further, the problem of interpretability of estimators in the sense of the inequality (3.1) exists; it is shown that all mentioned estimators are at least partially interpretable in the sense of requirements (3.2) or (3.10).     

Comparison of measuring devices

Although it is common to determine if two devices give the same results, we apply an affine transformation to make the two devices the same on the average. The device with a lower variability in its measurement results is more accurate. Repeated observations are required. The design is balanced if each object is measured the same number of times by each device. The properties this design yields justify this approach.     

Model for the distribution process of attitudes in a two-party-system

This article considers a social system where a political decision is to be made. Only two alternatives are permitted: YES or NO. Within the total population A there are two groups, one (X) campaigns for a YES decision, the other one (Y) argues for a NO decision. It is assumed that every individual within the total population has the same opportunities in the field of communications. The question to be answered is as follows: How are the opinions within the total population A distributed after a certain length of time. In our model we use a quantitative concept: The ‘Influence of Opinion in a Two-Party-System’. It is assumed that the relative influence of a group of people having a certain opinion is the stronger, the faster they are able to publicize their decision within the total population A. This and other assumptions (axioms) are formulated more precisely in the following discussion.     

On the detection of changes in autoregressive time series I. Asymptotics

Various test statistics are discussed which can be used for detecting changes in the parameters of an autoregressive time series. In this first part of our study, the limiting behavior of the test statistics is derived under the null hypothesis of no change as well as under alternatives. In a forthcoming second part of our investigation, these asymptotic results will be compared to some corresponding bootstrap procedures, and a small simulation study will be conducted.