We consider processes Xt with values in Lp(Ω, F, P) and "time" index t in a subset A of the unit cube. A natural condition of boundedness of increments is assumed. We give a full characterization of the domains A for which all such processes are a.e. continuous. We use the notion of Talagrand's majorizing measure as well as geometrical Paszkiewicz-type characteristics of the set A. A majorizing measure is constructed.
This paper is an attempt to explain variations across 261 regions of 27 EU countries in productivity growth for 2000-2013. The study is based on Fingleton's model which analyses the spatial process of productivity growth based on some elements of the theory of New Economic Geography and Endogenous Growth Theory. The applied specification links the productivity growth to the growth of output by means of Verdoorn's law. The model has been tested using the Spatial Panel Durbin Model with Multiple-Level Spatial Fixed Effects. Our findings suggest that increasing returns to scale are present in the EU economy. Moreover, the effect of increasing returns to scale is considerably stronger than has been suggested by both classic and recent research papers. Furthermore, we also find that there are evident spatial clusters of spatial productivity in the EU.
This paper revisits the theory of asymptotic behaviour of the well-known Gaussian Quasi-Maximum Likelihood estimator of parameters in mixed regressive, high-order autoregressive spatial models. We generalise the approach previously published in the econometric literature by weakening the assumptions imposed on the spatial weight matrix. This allows consideration of interaction patterns with a potentially larger degree of spatial dependence. Moreover, we broaden the class of admissible distributions of model residuals. As an example application of our new asymptotic analysis we also consider the large sample behaviour of a general group effects design.
We describe a new model of multiple reinsurance. The main idea is that the reinsurance premium is paid conditionally. It is motivated by some analysis of the ultimate price of the reinsurance contract. For simplicity we assume that the underlying risk pricing functional is the L2-norm. An unexpected relation to the general theory of sample regularity of stochastic processes is given.
When investigating healthcare efficiency at the regional level, the problem of interactions between neighbouring locations arises. The health of the population in a given region is related to the healthcare in other areas through a medical tourism, a limited number of highly specialised institutions, competition between institutions, etc. Ignoring these inter-regional links may result in a systematic bias in the efficiency analysis. Similar issues may hinder any regional studies. Hence, the main purpose of this paper is to introduce a new approach to measuring efficiency in regional studies through spatial data envelopment analysis (SDEA). The paper offers a proper mathematical formulation of the new methodology and highlights differences between classic data envelopment analysis (DEA) and the newly developed method. The motivation for seeking a new solution to the problem of spatially adequate assessment of regional efficiency is derived from the literature review and a discussion of the presented theoretical examples. The classic DEA allows for multidimensional analysis of the performance of homogenous independent decision-making units. However, in regional studies, an area where DEA has gained popularity, the assumption of the isolation of decision-making units seems to be unfounded. In the SDEA approach, the region-specific spatial context is incorporated into the analysis via the W matrix and spatial interactions are reflected in the model through spatially weighted inputs and outputs. Therefore, in our paper, we verify the hypothesis that spatial interactions are an indispensable factor of regional efficiency analysis. A study of healthcare efficiency in European regions is presented as an illustration of the utility of the new methodology. Furthermore, we compare the results of the classic DEA approach with those of the SDEA, which is augmented with the spatial equivalents of inputs and outputs. Our results suggest that classic DEA undervalues regional healthcare efficiency by underestimating the region-specific spatial context.2 Researchers may find the introduced SDEA method useful in all space related fields when investigated phenomenon exhibits spatial autocorrelation. In particular, the new approach may deepen the regional efficiency analysis of innovation, development, logistics, tourism, etc.
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