title: Confidence analysis of standard deviational ellipse and its extension into higher dimensional euclidean space.
abstract: Standard deviational ellipse (SDE) has long served as a versatile GIS tool for delineating the geographic distribution of concerned features. This paper firstly summarizes two existing models of calculating SDE, and then proposes a novel approach to constructing the same SDE based on spectral decomposition of the sample covariance, by which the SDE concept is naturally generalized into higher dimensional Euclidean space, named standard deviational hyper-ellipsoid (SDHE). Then, rigorous recursion formulas are derived for calculating the confidence levels of scaled SDHE with arbitrary magnification ratios in any dimensional space. Besides, an inexact-newton method based iterative algorithm is also proposed for solving the corresponding magnification ratio of a scaled SDHE when the confidence probability and space dimensionality are pre-specified. These results provide an efficient manner to supersede the traditional table lookup of tabulated chi-square distribution. Finally, synthetic data is employed to generate the 1-3 multiple SDEs and SDHEs. And exploratory analysis by means of SDEs and SDHEs are also conducted for measuring the spread concentrations of Hong Kong's H1N1 in 2009.
authors.affiliation: Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China.
authors.forename: Bin
authors.initials: B
authors.lastname: Wang
authors.affiliation: Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China.
authors.forename: Wenzhong
authors.initials: W
authors.lastname: Shi
authors.affiliation: Department of Land Surveying and Geo-Informatics, The Hong Kong Polytechnic University, Kowloon, Hong Kong, China.
authors.forename: Zelang
authors.initials: Z
authors.lastname: Miao
mesh_terms: D000465:Algorithms; D006723:Hong Kong / Q000453:epidemiology; D006801:Humans; D053118:Influenza A Virus, H1N1 Subtype; D007251:Influenza, Human / Q000453:epidemiology; D008962:Models, Theoretical; D011336:Probability