| We consider research in four related areas: robust parameter estimation, robust parameter estimation for generalized Gaussian, robust detection with parameter estimation and robust linear estimation of random variables.; For Chapter II, we apply a differential geometric approach toward robust parameter estimation, and we note that the results have application in many areas of communications and signal processing. In particular, we make a number of estimators (typically unbiased) of practical interest which include the variance associated with a Gaussian distribution, the standard deviation for a Laplace distribution, the variance of Rayleigh distribution and a “spread parameter” for a Cauchy distribution, which will all be presented. Finally, we measure inverse MSE and robustness together using a cost criterion and design robust estimators which optimize a mix of performance (inverse MSE) and robustness specified by the user.; For Chapter III, we apply robust estimation to generalized Gaussian family and find out how the MSE changes as the actual distribution varies over this family.; For Chapter IV, we apply a robust parameter estimation algorithm to design the ML (Maximum Likelihood) detector and we also consider the censored linear detector. For nominally i.i.d. N(O,1) noise, we calculate the performance β (detection probability) of each detector for perturbations of the noise distribution which are i.i.d. Gaussian and Laplace for a variety of variances. We also consider various signal values and numbers of samples, thus admitting a comparison of the performance and robustness of the two detectors for noise from moderate to heavy tailed.; For Chapter V, we consider the linear estimation of a random variable based on a realization of another random variable. We first note that a standard MSE criterion leads automatically to a complete lack of robustness, and that this is a consequence of the MSE criterion itself rather than the choice of estimator. We therefore consider an alternative fidelity criterion and show that it is possible in certain cases for minimum MSE and maximum robustness to be simultaneously achieved by the same estimator under this criterion. |
