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

機構典藏 > College of Sciences > Graduate Institute & Department of Mathematics > Journal Article > Item 987654321/106939

Please use this identifier to cite or link to this item: https://tkuir.lib.tku.edu.tw/dspace/handle/987654321/106939

Title:	A Note on the Frequency Polygon Based on the Weighted Sums 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;Primary 62G07;Secondary 62G20
Date:	2014-03-28
Issue Date:	2016-08-15
Abstract:	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.
Relation:	Communications in Statistics - Theory and Methods 43(8), pp.1666-1685
DOI:	10.1080/03610926.2012.673675
Appears in Collections:	[Graduate Institute & Department of Mathematics] Journal Article

Files in This Item:

File	Description	Size	Format
A Note on Frequency Polygon Based on Weighted Sum of Binned Data.pdf		643Kb	Adobe PDF	165	View/Open
index.html		0Kb	HTML	418	View/Open