Showing papers on "Robustness (computer science) published in 1971"

A General Qualitative Definition of Robustness

Abstract: Two very closely related definitions of robustness of a sequence of estimators are given which take into account the types of deviations from parametric models that occur in practice. These definitions utilize the properties of the Prokhorov distance between probability distributions. It is proved that weak $^\ast$-continuous functionals on the space of probability distributions define robust sequences of estimators (in either sense). The concept of the "breakdown point" of a sequence of estimators is defined, and some examples are given.

Robust detection of a known signal in nearly Gaussian noise

Abstract: A detector that is not nonparametric, but that nevertheless performs well over a broad class of noise distributions is termed a robust detector. One possible way to obtain a certain degree of robustness or stability is to look for a min-max solution. For the problem of detecting a signal of known form in additive, nearly Gaussian noise, the solution to the min-max problem is obtained when the signal amplitude is known and the nearly Gaussian noise is specified by a mixture model. The solution takes the form of a correlator-limiter detector. For a constant signal, the correlator-limiter detector reduces to a limiter detector, which is shown to be robust in terms of power and false alarm. By adding a symmetry constraint to the nearly normal noise and formulating the problem as one of local detection, the limiter-correlator is obtained as the local min-max solution. The limiter-correlator is shown to be robust in terms of asymptotic relative efficiency (ARE). For a pulse train of unknown phase, a limiter-envelope sum detector is also shown to be robust in terms of ARE.

Robust Procedures for Estimating Polynomial Regression

Abstract: In this article we seek good estimators and designs for estimating a regression function, when the function is assumed to be a polynomial of given degree plus a “small” polynomial of given higher degree. We propose a procedure using designs and estimators which are linear combinations of standard designs and estimators, and verify that in the cases computed our procedure shows desirable robustness properties when compared with the standard procedure.

Approximate Best Linear Prediction of a Certain Class of Stationary and Nonstationary Noise-Distorted Signals

Abstract: A technique for approximating the best linear predictor of a noise-distorted signal is presented. The technique is applicable when the signal is stationary with a spectrum which is highly concentrated around known or estimated frequencies, or when the signal is an accumulating sequence whose “spectrum” has poles at these frequencies. The noise must be stationary, but its spectrum need only be known or estimated at the above-mentioned frequencies. The time parameter is assumed to be discrete. Computer-generated data are then used to obtain an idea of the “robustness” of the technique.