A Note on the Frequency Polygon Based on the Weighted Sums of Binned Data

doi:10.1080/03610926.2012.673675

淡江大學機構典藏 > 商管學院 > 公共行政學系暨研究所 > 期刊論文 > Item 987654321/113015

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題名:	A Note on the Frequency Polygon Based on the Weighted Sums 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:	2014-03-28
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:	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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