On the influence of sample set structure on decision rule quality for the case of a linear discriminant function

The influence of sample set structure on decision rule quality for the case of a linear discriminant function is considered. Specifically, the case of missing data in the sample set and the case when the multivariate random variable is to be registered with the help of a single-channel device are investigated. Some rather unusual phenomena are discussed, such as when some new samples are added to the sample set, and as a result the quality of parameter estimations used in a decision rule become better, but at the same time the quality of the decision rule itself becomes worse. The investigation is performed for the classical model of a twocategory classifier when the categories are described by the multivariate normal densities having common covariance matrices. Some results of statistical simulation experiments are included.