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    Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/113015


    Title: A Note on Frequency Polygon Based on Weighted Sum of Binned Data
    Authors: Deng, Wen-Shuenn;Wu, Jyh-Shyang;Chen, Li-Ching;Ke, Shun-Jie
    Keywords: Edge frequency polygon;Kernel-based weights;Midpoint frequency polygon;Minimum variance weights;Mixture weights;Uniform weights
    Date: 2014-03-28
    Issue Date: 2018-03-29 12:10:44 (UTC+8)
    Abstract: We revisit the generalized midpoint frequency polygons of Scott (1985), and the edge frequency polygons of Jones et al. (1998 Jones, M.C., Samiuddin, M., Al-Harbey, A.H., Maatouk, T. A.H. (1998). The edge frequency polygon. Biometrika 85:235–239.
    [Crossref], [Web of Science ®], [Google Scholar]
    ) and Dong and Zheng (2001 Dong, J.P., Zheng, C. (2001). Generalized edge frequency polygon for density estimation. Statist. Probab. Lett. 55:137–145.
    [Crossref], [Web of Science ®], [Google Scholar]
    ). 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 of minimizing 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.
    Relation: Communications in Statistics – Theory and Methods 43(8), p.1666-1685
    DOI: 10.1080/03610926.2012.673675
    Appears in Collections:[Graduate Institute & Department of Public Administration] Journal Article

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