| This dissertation investigates new parametric and nonparametric bounds on the Bayes risk that can be used as a criterion in feature selection and extraction in radar target identification (RTI).; For the parametric case, where the form of the underlying statistical distributions is known, Bayesian decision theory offers a well-motivated methodology for the design of parametric classifiers. This investigation provides new bounds on the Bayes risk for both simple and composite classes. Bounds on the Bayes risk for M classes are derived in terms of the risk functions for (M - 1) classes, and so on until the result depends on the Pairwise Bayes risks.; When the parameters of the underlying distributions are unknown, an analysis of the effect of finite sample size and dimensionality on these bounds is given for the case of supervised learning. For the case of unsupervised learning, the parameters of these distributions are evaluated by using the maximum likelihood technique by means of an iterative method and an appropriate algorithm.; Finally, for the nonparametric case, where the form of the underlying statistical distributions is unknown, a nonparametric technique, the nearest-neighbor (N N) rule, is used to provide estimated bounds on the Bayes risk. Two methods are proposed to produce a finite sample size risk close to the asymptotic one. The difference between the finite sample size risk and the asymptotic risk is used as the criterion of improvement. |
