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**Asymptotic properties of the remedian.**
*(English)*
Zbl 1055.62019

Summary: The remedian method is a robust and storage-saving procedure for computing a central summary value of a huge data set. It mimics an ordinary sample median in many ways but needs only \(bk\) storage spaces for a sample of size \(n=b^k\). We investigate the large sample properties of the remedian method. It is shown that the remedian with any \(b\) and \(k\) such that \(n=b^k\), as an estimator of the population median, is strongly consistent as \(n\to\infty\). Furthermore, if both \(b\) and \(k\) tend to \(\infty\) as \(n\to\infty\), the convergence rate is only slightly lower than the ordinary rate \(n^{-1/2}\), and the distribution of the remedian, while appropriately normalized, approaches the normal distribution. Therefore, the large sample study leads to the conclusion that the remedian method with appropriate choices of \(b\) and \(k\) does not lose much efficiency compared with the ordinary median method while dramatically reducing the storage space in computation and sustaining the robustness of median to a certain extent.

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\textit{H. Chen} and \textit{Z. Chen}, J. Nonparametric Stat. 17, No. 2, 155--165 (2005; Zbl 1055.62019)

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### References:

[1] | Rousseeuw PJ, Journal of the American Statistical Association 85 pp 97– (1990) · Zbl 0702.62030 |

[2] | DOI: 10.1214/ss/1009212753 |

[3] | Chao MT, Journal of Statistical Planning and Inference 37 pp 1– (1993) · Zbl 0780.62015 |

[4] | Kaczor WJ, Problems in Mathematical Analysis I: Real Numbers, Sequences and Series (1996) |

[5] | Reiss R-D, Approximation Distributions of Order Statistics (1989) · Zbl 0682.62009 |

[6] | Chen Z, Statistica Sinica 11 pp 23– (2001) |

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