Quasi-measures with image transformations as generalized variables
The author introduces the notion of an image transformation and studies its properties to investigate whether the quasi-probability constructed by an image transformation could serve as a model for median and sample median in probability theory. In Section~2, it is shown that an image transformation naturally induces a mapping from probability measures into quasi-probability measures. In Section~3, a structure theorem for image transformations is given and as its consequence it is proved that image transformations defined only on solid sets extend uniquely to image transformations on all open or closed sets. In Section~4, the multidimensional median and sample median are presented as image transformations. Preservation (equivariance in statistical literature) properties of the medians are also given.
scientific article; zbMATH DE number 1836736