The Empirical Bayes Classification Rules for Mixtures of Discrete and Continuous Variables

✍ Scribed by T. Wojciechowski

• Publisher: John Wiley and Sons
• Year: 1985
• Tongue: English
• Weight: 603 KB
• Volume: 27
• Category: Article
• ISSN: 0323-3847
• DOI: 10.1002/bimj.4710270507

✦ Synopsis

Let us consider a general population R. Each object belonging to the population R is characterized by a pair of correlated random vectors (& I). Both X and _Y may be mixtures of discrete and continuous random variables. It will be assumed that our population R consists of k groups nl, ..., 3zk, which depend on the value of the random vector 1. A certain object, which is an element of one of the k groups ni, ..., nk, has to be classified into the correct group. The knowledge of the value of the random vector would permit its correct classification, but the observation of this vector is difficult or dangerous and we must assign the individual on the basis of the observation of the random vector X. The classification procedure is based on randomized decision function 6* which minimizes the risk function i.e. Bayes decision function. We give also two empirical Bayes classification rules i.e. decision functions based on the sample from popula+ion n and having property that their risks converge t o Bayes risk when the sample size increases.