The classical distributed sparse regression based on least square error is sensitive to the outliers in the desired data. In this manuscript, we consider the rank based estimator named minimum Wilcoxon norm for developing robust non-parametric sparse regression over distributed adaptive networks. The convergence analysis of the proposed algorithm is analyzed using asymptotic linearity of rank test. Exhaustive simulation studies show that the proposed methods are robust against outliers in the desired data and exploits sparsity, hence performs better than the existing methods if the parameter of interest is sparse. The proposed algorithms are validated for three different applications namely distributed parameter estimation, tracking and distributed power spectrum estimation.

基于最小二乘误差的经典分布式稀疏回归对所需数据中的异常值敏感。在本文中，我们考虑了基于秩的估计器，即最小Wilcoxon范数，用于在分布式自适应网络上开发鲁棒的非参数稀疏回归。利用秩检验的渐近线性分析了该算法的收敛性。详尽的仿真研究表明，所提出的方法对所需数据中的异常值具有鲁棒性，并且具有稀疏性，因此，如果感兴趣的参数稀疏，则其性能将优于现有方法。所提出的算法针对三种不同的应用进行了验证，即分布式参数估计，跟踪和分布式功率谱估计。