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Statistically (optimal) estimators of semivariance: A correction of Josephy-Aczel’s proof

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Fleischer K., Nietert B.
Śląski Przegląd Statystyczny
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2019
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issue 17 (23)
9-30
EN
Semivariance is an intuitive risk measure because it concentrates on the shortfall below a target and not on total variation. To successfully use semivariance in practice, however, a statistical estimator of semivariance is needed; Josephy and Aczel provide such an estimator. Unfortunately, they have not correctly proven asymptotic unbiasedness and mean squared error consistency of their estimator since their proof contains a mistake. This paper corrects the computational mistake in Josephy-Aczel’s original proof and, that way, allows researchers and practitioners in the field of downside portfolio selection, hedging, downside asset pricing, risk measurement in a regulatory context, and performance measurement to work with a meaningfully specified downside measure.
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The size of the basic unit in geographical analysis

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Suchożebrski J., Kwiatkowska J. M.
Miscellanea Geographica. Regional Studies on Development
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2004
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vol. 11
151-160
EN
In geographical analysis such as mathematical classification and modeling, the study area is divided into a network of basic (quasi-homogenous) units. A technique often used in the delimitation of the basic unit to be analyzed is the division of the study area into a network of uniform geometrical figures (block-centered grid). This article presents two objective methods for dividing the surface area of the study region into a network of basic units. The geometric method makes it possible to determine the optimal size of the basic unit, relative to the surface area being analyzed. This method may be used in analysis conducted on a regional scale, in which case the analysis and the results are characterized by a greater degree of generalization. Geostatistical methods (semivariance analysis and nearest-neighbor analysis) make it possible to determine the size of the cell in the grid of quasi-homogenous units, based on the spatial variation of elements in the natural environment and on the placement of data points. These methods can be recommended for the analysis of small areas (e.g. small drainage areas), when highly detailed data and results are required.
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