Classification based on hybridization of parametric and nonparametric classifiers

Parametric methods of classification assume specific parametric models for competing population densities (e.g., Gaussian population densities can lead to linear and quadratic discriminant analysis) and they work well when these model assumptions are valid. Violation in one or more of these parametric model assumptions often leads to a poor classifier. On the other hand, nonparametric classifiers (e.g., nearest-neighbor and kernel-based classifiers) are more flexible and free from parametric model assumptions. But, the statistical instability of these classifiers may lead to poor performance when we have small numbers of training sample observations. Nonparametric methods, however, do not use any parametric structure of population densities. Therefore, even when one has some additional information about population densities, that important information is not used to modify the nonparametric classification rule. This paper makes an attempt to overcome these limitations of parametric and nonparametric approaches and combines their strengths to develop some hybrid classification methods. We use some simulated examples and benchmark data sets to examine the performance of these hybrid discriminant analysis tools. Asymptotic results on their misclassification rates have been derived under appropriate regularity conditions.