Approaches and algorithms for robust signal processing

The development of approaches and algorithms for robust signal processing are discussed. Robust signal processing, refers to the problem of smoothing, filtering or estimating noisy and unknown signals. The linear estimation problem in the formalism of linear regression is considered. The specific problem of filtering or smoothing a discrete time sequence is considered and a new method is proposed. This method is compared to more traditional methods in a Monte Carlo study. A new algorithm is presented which called the ABC algorithm, to compute a variant of the Huber regression estimate. An extensive Monte Carlo study of the corresponding location estimate is presented. The ABC algorithm is a partitioning algorithm and allows for exact computations. Its important theoretical consequences for linear programming are discussed. The problem of calculating the densities of order statistics and statistics derived from them is considered. A new algorithm is presented which allows the random variables to be nonidentically distributed.