Linear minimax regret estimation of deterministic parameters with bounded data uncertainties

We develop a new linear estimator for estimating an unknown parameter vector x in a linear model in the presence of bounded data uncertainties. The estimator is designed to minimize the worst-case regret over all bounded data vectors, namely, the worst-case difference between the mean-squared error (MSE) attainable using a linear estimator that does not know the true parameters x and the optimal MSE attained using a linear estimator that knows x. We demonstrate through several examples that the minimax regret estimator can significantly increase the performance over the conventional least-squares estimator, as well as several other least-squares alternatives.