A Note on the Frequency Polygon Based on the Weighted Sum of Binned Data
學年 102
學期 2
出版(發表)日期 2014-03-28
作品名稱 A Note on the Frequency Polygon Based on the Weighted Sum of Binned Data
著者 Wen-Shuenn Deng; Jyh-Shyang Wu; Li-Ching Chen; Shun-Jie Ke
著錄名稱、卷期、頁數 Communications in Statistics – Theory and Methods 43(8), p.1666-1685
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.
關鍵字 Edge frequency polygon;Kernel-based weights;Midpoint frequency polygon;Minimum variance weights;Mixture weights;Uniform weights
語言 en_US
ISSN 1532-415X
期刊性質 國外
收錄於 SCI
通訊作者 Deng, Wen-shuenn
國別 USA
出版型式 ,電子版,紙本

機構典藏連結 ( http://tkuir.lib.tku.edu.tw:8080/dspace/handle/987654321/113015 )