The mastering of complexity as a problem of the Social Sciences

The main purpose of this paper is the old methodological problem of the mastering of complexity in the Social Sciences. In sociology the traditional solution is displayed by some methods for the external reduction of complexity. Although some authors in the history of sociology tried to formulate a heuristic program for an empirical-analytical action science, they finally became victims of their own criticism of previous sociology: to simplify the social reality instead of establishing an increasing capacity of complexity for societal-theory building. This more historical aspect and first part of this paper is followed by some newer methodological reflections: to increase the capacity of complexity by a strategy of internal reduction of complexity or better: internal complexity processing. Instead of simplification the strategy of differentiation is proposed.     

Forecasting Vector ARMA Processes With Systematically Missing Observations

The following two predictors are compared for time series with systematically missing observations: (a) A time series model is fitted to the full series X_t , and forecasts are based on this model, (b) A time series model is fitted to the series with systematically missing observations Y _τ, and forecasts are based on the resulting model. If the data generation processes are known vector autoregressive moving average (ARMA) processes, the first predictor is at least as efficient as the second one in a mean squared error sense. Conditions are given for the two predictors to be identical. If only the ARMA orders of the generation processes are known and the coefficients are estimated, or if the process orders and coefficients are estimated, the first predictor is again, in general, superior. There are, however, exceptions in which the second predictor, using seemingly less information, may be better. These results are discussed, using both asymptotic theory and small sample simulations. Some economic time series are used as illustrative examples.     

Computation of the percentage points and the power for the two-sided Kolmogorov-Smirnov one sample test

Two recursive schemes are presented for the calculation of the probabilityP(g(x)≤S _n (x)≤h(x) for allx∈®), whereS _n is the empirical distribution function of a sample from a continuous distribution andh, g are continuous and isotone functions. The results are specialized for the calculation of the distribution and the corresponding percentage points of the test statistic of the two-sided Kolmogorov-Smirnov one sample test. The schemes allow the calculation of the power of the test too. Finally an extensive tabulation of percentage points for the Kolmogorov-Smirnov test is given.     

Credibility, Information Preferences, and Information Interests

The Seveso Directive of the European Union demands that information be provided to the public by companies and authorities about facts, risks, and behaviors related to hazardous facilities, in particular chemical facilities. On behalf of the Commission of the European Communities, a survey was run in five European countries on the credibility of various information sources. This article describes the results of the German study. 430 persons were interviewed with a questionnaire of 50 items, in particular about their perceptions and evaluations of technical risks, the credibility of sources of information about chemical risks, their preferences for receiving risk information from these sources, and their interests in receiving information. Major findings are great differences in credibility, differentiated information preferences, and strong information interests. Surprisingly, credibility played only a minor role with regard to the respondents'information preferences and interests.     

Global Environmental Change and Historical Transitions

What do transition processes in rural areas in Thailand, biomass consumption in nineteenth-century Austria and the ecology of hunter-gatherers have to do with the appropriation of plant production and global environmental change? More than one might think of in the first place. They are part of a scholarly discourse on our changing relations with the environment. We argue that global change can be analysed in terms of transitions between major modes of subsistence and try to document this with several case studies.     

The cost of not knowing the radius

Robust Statistics considers the quality of statistical decisions in the presence of deviations from the ideal model, where deviations are modelled by neighborhoods of a certain size about the ideal model. We introduce a new concept of optimality (radius-minimaxity) if this size or radius is not precisely known: for this notion, we determine the increase of the maximum risk over the minimax risk in the case that the optimally robust estimator for the false neighborhood radius is used. The maximum increase of the relative risk is minimized in the case that the radius is known only to belong to some interval [r _l ,r _u ]. We pursue this minmax approach for a number of ideal models and a variety of neighborhoods. Also, the effect of increasing parameter dimension is studied for these models. The minimax increase of relative risk in case the radius is completely unknown, compared with that of the most robust procedure, is 18.1% versus 57.1% and 50.5% versus 172.1% for one-dimensional location and scale, respectively, and less than 1/3 in other typical contamination models. In most models considered so far, the radius needs to be specified only up to a factor , in order to keep the increase of relative risk below 12.5%, provided that the radius–minimax robust estimator is employed. The least favorable radii leading to the radius–minimax estimators turn out small: 5–6% contamination, at sample size 100.