Optimal and Robust Memoryless Discrimination from Dependent Observations
Abstract
Memoryless discrimination is a method for binary hypothesis testing in which a test statistic is computed by passing each observation through a memoryless nonlinearity and summing the outputs. Under certain conditions, including a mixing condition on the observed process, such a test statistic becomes asymptotically Gaussian, thus permitting the error probabilities to be approximated. In this thesis, asymptotic performance measures are derived as functionals of the nonlinearities, and in this way memoryless discrimination is well formulated as an optimization problem. Both the Neyman-Pearson and minimax problems are considered. In all, four different performance measures are derived under different problem formulations, and in each case, the optimal nonlinearity is shown to be the solution of an integral equation. Results for minimax robustness are presented for three of the performance measures. Performance results from numerical simulations for each of the nonlinearities derived here as well as the optimal iid nonlinearity are presented and discussed.
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 09, 1988
- Accession Number
- ADA202671
Entities
People
- Douglas W. Sauder
Organizations
- United States Naval Research Laboratory