Please use this identifier to cite or link to this item: https://doi.org/10.1080/1048525042000267798
Title: Asymptotic properties of the remedian
Authors: Chen, H.
Chen, Z. 
Keywords: Asymptotic normality
Median
Robustness
Storage space
Strong consistency
Issue Date: Mar-2005
Citation: Chen, H., Chen, Z. (2005-03). Asymptotic properties of the remedian. Journal of Nonparametric Statistics 17 (2) : 155-165. ScholarBank@NUS Repository. https://doi.org/10.1080/1048525042000267798
Abstract: 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. In this article, we investigate the large sample properties of the remedian method. It is shown that the remedian with any b and k such that n = bk, as an estimator of the population median, is strongly consistent as n → ∞. Furthermore, if both b and k tend to ∞ as n → ∞, 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.
Source Title: Journal of Nonparametric Statistics
URI: http://scholarbank.nus.edu.sg/handle/10635/105028
ISSN: 10485252
DOI: 10.1080/1048525042000267798
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