Statistically (optimal) estimators of semivariance: A correction of Josephy-Aczel’s proof - Fleicher, Karlheinz; Nietert, Bernhard (Optymalne estymatory semiwariancji: korekta dowodu Josephy’ego-Aczela, 2019)
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
Śląski Przegląd Statystyczny = Silesian Statistical Review, 2019, Nr 17 (23), s. 9-29
Keywords: risk analysis; semivariance; statistical estimation; analiza ryzyka; semiwariancja; estymacja statystyczna