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    請使用永久網址來引用或連結此文件: http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/113015

    題名: A Note on Frequency Polygon Based on Weighted Sum of Binned Data
    作者: Deng, Wen-Shuenn;Wu, Jyh-Shyang;Chen, Li-Ching;Ke, Shun-Jie
    關鍵詞: Edge frequency polygon;Kernel-based weights;Midpoint frequency polygon;Minimum variance weights;Mixture weights;Uniform weights
    日期: 2014-04
    上傳時間: 2018-03-29 12:10:44 (UTC+8)
    摘要: 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.
    關聯: Communications in Statistics – Theory and Methods 43(8), p.1666-1685
    DOI: https://doi.org/10.1080/03610926.2012.673675
    顯示於類別:[公共行政學系暨研究所] 期刊論文


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