Robustness and power of parametric, nonparametric, robustified and adaptive tests—The multi-sample location problem

This paper deals with a survey of different types of tests, parametric, nonparametric, robustified and adaptive ones, and with an application to the two-sided c-sample location problem. Some concepts of robustness are discussed, such as breakdown point, influence function, gross-error sensitivity and especially α- and β-robustness. A robustness study on level α in the case of heteroscedasticity and nonnormal distributions is carried out via Monte Carlo methods and also a power comparison of all the tests considered. It turns out that robustified versions of the F-test and Welch-test where the original observations are replaced by its ranks behave well over a broad class of distributions, symmetric ones with different tail weight and asymmetric ones, but, on the whole, an adaptive test is to prefer.     

Quadratic programming applications

Although quadratic programming (QP) is often studied as a methodology by decision scientists, little emphasis seems to be given to the type of decision science problems that can be so modeled. This paper reviews and extends some of the applied and methodological areas where QP is applicable, discussing and illustrating the characteristics and aspects of the accompanying solutions. Some of the methodological areas amenable include regression analysis, decision analysis, and quadratic approximations to generally complex functions. In the functional management areas, QP is applicable to problems in economics, such as demand-supply response and enterprise selection. In finance, it is used in portfolio analysis; in agriculture, in crop selection. Both the methodological and functional applications of QP are reviewed. Potential new applications of QP are suggested.