摘要翻译:
我们导出了回归的MM-估计和约束M-估计或CM-估计的最大偏差函数,并将它们与回归的S-估计和$\tau$-估计的最大偏差函数进行了比较。在这些比较中,CM估计往往表现出最有利的偏差稳健性性质。此外,在高斯模型下,我们还证明了如何构造一个具有比给定S-估计更小的最大偏差函数的CM-估计,即所得到的CM-估计在最大偏差方面优于S-估计,同时也大大提高了效率。
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英文标题:
《On the maximum bias functions of MM-estimates and constrained
M-estimates of regression》
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作者:
Jos\'e R. Berrendero, Beatriz V. M. Mendes, David E. Tyler
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最新提交年份:
2007
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分类信息:
一级分类:Mathematics 数学
二级分类:Statistics Theory 统计理论
分类描述:Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计:例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类:Statistics 统计学
二级分类:Statistics Theory 统计理论
分类描述:stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近,贝叶斯推论,决策理论,估计,基础,推论,检验。
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英文摘要:
We derive the maximum bias functions of the MM-estimates and the constrained M-estimates or CM-estimates of regression and compare them to the maximum bias functions of the S-estimates and the $\tau$-estimates of regression. In these comparisons, the CM-estimates tend to exhibit the most favorable bias-robustness properties. Also, under the Gaussian model, it is shown how one can construct a CM-estimate which has a smaller maximum bias function than a given S-estimate, that is, the resulting CM-estimate dominates the S-estimate in terms of maxbias and, at the same time, is considerably more efficient.
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PDF链接:
https://arxiv.org/pdf/708.039