Nonparametric Implications of Random Conversion of Discontinuous Data to Nearly Equivalent Continuous Form

摘要

This paper contains an extensive consideration of general approach for converting discontinuous data to almost equivalent continuous form outlined in previous works with respect to nonparametric uses. Both the theoretical and application aspects are discussed. In some cases, the property investigated is exactly preserved by the conversion. Several examples are given of such cases. Often, the change in the property being investigated (due to the conversion to continuous data) is unimportant. Even when the change is important, bounded probability results can sometimes be obtained by suitable conversion of the data to continuous form. An example is given that illustrates this kind of application. (Author)