On Huber's contaminated model

IF 1.8 2区数学 Q1 MATHEMATICS

Journal of Complexity Pub Date : 2023-08-01 DOI:10.1016/j.jco.2023.101745

Weiyan Mu , Shifeng Xiong

引用次数: 0

Abstract

Huber's contaminated model is a basic model for data with outliers. This paper aims at addressing several fundamental problems about this model. We first study its identifiability properties. Several theorems are presented to determine whether the model is identifiable for various situations. Based on these results, we discuss the problem of estimating the parameters with observations drawn from Huber's contaminated model. A definition of estimation consistency is introduced to handle the general case where the model may be unidentifiable. This consistency is a strong robustness property. After showing that existing estimators cannot be consistent in this sense, we propose a new estimator that possesses the consistency property under mild conditions. Its adaptive version, which can simultaneously possess this consistency property and optimal asymptotic efficiency, is also provided. Numerical examples show that our estimators have better overall performance than existing estimators no matter how many outliers in the data.

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关于Huber污染模型

Huber污染模型是具有异常值的数据的基本模型。本文旨在解决该模型的几个基本问题。我们首先研究了它的可识别性性质。给出了几个定理来确定模型在各种情况下是否可识别。基于这些结果，我们讨论了用Huber污染模型的观测值估计参数的问题。引入了估计一致性的定义来处理模型可能不可识别的一般情况。这种一致性是一种强鲁棒性。在证明了现有的估计量在这个意义上不可能是一致的之后，我们提出了一个在温和条件下具有一致性性质的新估计量。同时给出了它的自适应版本，它可以同时具有这种一致性和最优渐近效率。数值例子表明，无论数据中有多少异常值，我们的估计量都比现有的估计量具有更好的总体性能。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Complexity 工程技术-计算机：理论方法

CiteScore

3.10

自引率

17.60%

发文量

审稿时长

>12 weeks

期刊介绍： The multidisciplinary Journal of Complexity publishes original research papers that contain substantial mathematical results on complexity as broadly conceived. Outstanding review papers will also be published. In the area of computational complexity, the focus is on complexity over the reals, with the emphasis on lower bounds and optimal algorithms. The Journal of Complexity also publishes articles that provide major new algorithms or make important progress on upper bounds. Other models of computation, such as the Turing machine model, are also of interest. Computational complexity results in a wide variety of areas are solicited. Areas Include: • Approximation theory • Biomedical computing • Compressed computing and sensing • Computational finance • Computational number theory • Computational stochastics • Control theory • Cryptography • Design of experiments • Differential equations • Discrete problems • Distributed and parallel computation • High and infinite-dimensional problems • Information-based complexity • Inverse and ill-posed problems • Machine learning • Markov chain Monte Carlo • Monte Carlo and quasi-Monte Carlo • Multivariate integration and approximation • Noisy data • Nonlinear and algebraic equations • Numerical analysis • Operator equations • Optimization • Quantum computing • Scientific computation • Tractability of multivariate problems • Vision and image understanding.