A statistical decision rule with incomplete knowledge about classes

摘要

A statistical decision rule among M classes is presented when the a priori knowledge about classes is not complete: either the number of classes is not the true one, or it is not possible to obtain samples from all the possible classes. The reject option proposed by Chow is extended by defining an ambiguity reject option and a distance reject option. These two types of reject can be defined in a parametric as well as in a non-parametric way. An example is given in R in order to illustrate this rule. This method has been developed essentially to solve diagnostic problems.