Parameter estimation in linear models based on outage probability minimization

A traditional approach to estimating random unknown signal parameters in a noisy linear model aims at minimizing the mean squared error (MSE) averaged over both the random signal parameters and noise realizations. In this paper, we develop a new estimation approach which minimizes the MSE averaged over the noise only. Moreover, in contrast to the traditional approach, the MSE is minimized only for the most favorable signal parameter realizations. It is assumed that the second- order statistics of the unknown signal parameter and noise vectors are precisely known and the noise is Gaussian, while the probability density function (pdf) of the unknown signal parameter vector may be Gaussian or completely unknown. Two different linear estimators are derived for the latter two cases.