Robust Estimation of Block-Error Ratio under Excessive Noise Based on Empirical Probability Generating Function

Abstract

The paper presents construction of a highly robust estimator for block-error ratio in the binomial transmission model under heavy additional noise or disturbances. The estimator is based on the empirical probability generating function computed at single point in the transform domain. Such construction leads to explicit expressions for influence function and asymptotic variance. The influence analysis explains why the estimator is notably useful when estimating small error probabilities and how to tune its performance in presence of gross outliers. While robustness comes often at the expense of increased bias, variance and/or computational effort, the proposed estimator is nearly unbiased, possibly very efficient, and easy to compute without processing the data or any optimization procedure. The last feature makes it attractive for automated real-time and online applications. The asymptotic arguments are validated in simulations for small and moderate sample sizes. Advantages over the sample median, the maximum likelihood estimator and the minimum Hellinger distance estimator in context of this application are discussed.