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在医学研究中,经常遇到受污染的数据。常用的经典统计分析方法对这些污染数据很敏感,并且结果也很不稳定,解决这个问题的途径之一就是采用稳健统计方法。稳健的含义是,当假设的分布与实际分布相差较远,或数据中存在污染时,稳健方法的结果要相对稳定,不能与实际情况相差太大。本文提出了一种新的稳健回归方法,并从理论上对其大样本性质进行了讨论,还通过计算机模拟对小样本性质进行了讨论,最后通过实例检验其实用价值。
In medical research, contaminated data is often encountered. The commonly used classical statistical analysis methods are very sensitive to these pollution data, and the results are also very unstable. One of the ways to solve this problem is to adopt robust statistical methods. The implication of soundness is that when the hypothesis distribution is far from the actual distribution or there is pollution in the data, the robust method results are relatively stable and cannot be too different from the actual situation. This paper presents a new robust regression method, and theoretically discusses its large-sample nature. It also discusses the nature of small samples through computer simulation, and finally tests its practical value through examples.