Estimation of Parameters for Gaussian Random Variables using Robust Differential Geometric Techniques
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Most signal processing systems today need to estimate parameters of the underlying probability distribution, however quantifying the robustness of this system has always been difficult. This thesis attempts to quantify the performance and robustness of the Maximum Likelihood Estimator (MLE), and a robust estimator, which is a Huber-type censored form of the MLE. This is possible using diff erential geometric concepts of slope. We compare the performance and robustness of the robust estimator, and its behaviour as compared to the MLE. Various nominal values of the parameters are assumed, and the performance and robustness plots are plotted. The results showed that the robustness was high for high values of censoring and was lower as the censoring value decreased. This choice of the censoring value was simplifi ed since there was an optimum value found for every set of parameters. This study helps in future studies which require quantifying robustness for di fferent kinds of estimators.