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    jsp.display-item.identifier=請使用永久網址來引用或連結此文件: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/106939

    题名: A Note on the Frequency Polygon Based on Weighted Sum of Binned Data
    作者: Deng, Wen-shuenn;Wu, Jyh-shyang;Chen, Li-ching;Ke, Shun-jie
    关键词: Edge frequency polygon;Kernel-based weights;Midpoint frequency polygon;Minimum variance weights;Mixture weights;Uniform weights;Primary 62G07;Secondary 62G20
    日期: 2014-03-28
    上传时间: 2016-08-15
    摘要: We revisit the generalized midpoint frequency polygons of Scott (1985), and the edge frequency polygons of Jones et al. (1998) and Dong and Zheng (2001). Their estimators are linear interpolants of the appropriate values above the bin centers or edges, those values being weighted averages of the heights of r, r ∈ N, neighboring histogram bins. We propose a simple kernel evaluation method to generate weights for binned values. The proposed kernel method can provide near-optimal weights in the sense ofminimizing asymptotic mean integrated square error. In addition, we prove that the discrete uniform weights minimize the variance of the generalized frequency polygon under some mild conditions. Analogous results are obtained for the generalized frequency polygon based on linearly prebinned data. Finally, we use two examples and a simulation study to compare the generalized midpoint and edge frequency polygons.
    關聯: Communications in Statistics - Theory and Methods 43(8), pp.1666-1685
    DOI: 10.1080/03610926.2012.673675
    显示于类别:[數學學系暨研究所] 期刊論文


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