We revisit the generalized midpoint frequency polygon if Scott(1985), and the edge frequency polygon of Jones et all. (1998) and Dong and Zheng (2001). Their estimators are liner 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 kernel evaluation method to genrate 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 yo compare the generalized midpoint and edge frequency polygons.
Communications in Statistics - Theory and Methods(In Press)