• Journal of the Korean Data and Information Science Society
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• v.23 no.4
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• pp.765-775
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• 2012

The cross-validation is a popular method to select bandwidth in all types of kernel estimation. The maximum likelihood cross-validation, the least squares cross-validation and biased cross-validation have been proposed for bandwidth selection in kernel density estimation. In the case that the probability density function has a discontinuity point, Huh (2012) proposed a method of bandwidth selection using the maximum likelihood cross-validation. In this paper, two forms of cross-validation with the one-sided kernel function are proposed for bandwidth selection to estimate the location and jump size of the discontinuity point of density. These methods are motivated by the least squares cross-validation and the biased cross-validation. By simulated examples, the finite sample performances of two proposed methods with the one of Huh (2012) are compared.

• Journal of the Korean Data and Information Science Society
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• v.23 no.1
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• pp.79-87
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• 2012

In the case that the probability density function has a discontinuity point, Huh (2002) estimated the location and jump size of the discontinuity point based on the difference between the right and left kernel density estimators using the one-sided kernel function. In this paper, we consider the cross-validation, made by the right and left maximum likelihood cross-validations, for the bandwidth selection in order to estimate the location and jump size of the discontinuity point. This method is motivated by the one-sided cross-validation of Hart and Yi (1998). The finite sample performance is illustrated by simulated example.

• Korean Journal of Environment and Ecology
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• v.27 no.1
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• pp.11-21
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• 2013

We tried to find out the core feeding site of the Red-crowned Crane(Grus japonensis) in Cheorwon, Korea by using analysis techniques which are MCP(minimum convex polygon), KDE(kernel density estimation), LoCoH(local nearest-neighbor convex-hull). And, We discussed the difference and meaning of result among analysis methods. We choose the data of utilization distribution from distribution map of Red-crowned Crane in Cheorwon, Korea at $17^{th}$ February 2012. Extent of the distribution area was $140km^2$ by MCP analysis. Extents of core feeding area of the Red-crowned Crane were $33.3km^2$($KDE_{1000m}$), $25.7km^2$($KDE_{CVh}$), $19.7km^2$($KDE_{LSCVh}$), according to the 1000m, CVh, LSCVh in value of bandwidth. Extent, number and shape complexity of the core area has decreased, and size of each core area have decreased as small as the bandwidth size(default:1000m, CVh: 554.6m, LSCVh: 329.9). We would suggest the CVh value in KDE analysis as a proper bandwidth value for the Red-crowned crane's core area zoning. Extent of the distribution range and core area have increased and merged into the large core area as a increasing of k value in LoCoH analysis. Proper value for the selecting core area of Red-crowned Crane's distribution was k=24, and extent of the core area was $18.2km^2$, 16.5% area of total distribution area. Finally, the result of LoCoH analysis, we selected two core area, and number of selected core area was smaller than selected area of KDE analysis. Exact value of bandwidth have not been used in studies using KDE analysis in most articles and presentations of the Korea. As a result, it is needed to clarify the exact using bandwidth value in KDE studies.