ROBUST ESTIMATION AND SIGNAL-DETECTION WITH DEPENDENT NONSTATIONARY DATA

In this paper the dual topics of robust signal detection and robust estimation of a random variable are considered, where the data may be both dependent and nonstationary. We note that classical saddlepoint techniques for robustness do not readily apply in the dependent and/or nonstationary situation, and thus our results have application in a larger; domain than what was feasible heretofore. In addition, our methods make possible the quantitative measurement of robustness and admit essentially arbitrary perturbations in an underlying joint statistical distribution away from the nominal. In particular, our methods show that the presence of dependency can result in a reduction of the robustness of the Linear detector by approximately 50% and that appropriate censoring can improve this situation. We also show that, somewhat surprisingly, a weak amount of censoring can actually reduce robustness rather than increase it, even with dependent data that is ''almost'' independent. This calls into question the common practice, inspired by classical saddlepoint results for independent data, of employing censoring in cases where residual dependency is conceded. When applied to estimation, our work shows that for nominally Gaussian data, the conditional expectation estimator is optimal not only in terms of performance but also robustness (under appropriate performance measures), thus reinforcing the appeal of this estimator. On the other hand, for other performance measures, we also note that the conditional expectation estimator can be completely unrobust, regardless of whether the data is nominally Gaussian or not. Finally, our results establish a bound on estimator robustness.