# 臺灣博碩士論文加值系統

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 Spatial statistics are mainly aimed to analyze spatial data which are oftencorrelated in space and are differentiated from typical data. While conduct-ing a spatial data analysis, observations that are suspicious (e.g. outliersand/or influential points) will cause problems. Such observations need tobe detected so that appropriate adjustments can be made to the analysis.Therefore, detection of such influential points in spatial data is essential. Inthis thesis, we first review two methods called spatial-statistic and scatter-plot for the outlier detection in spatial data. Then we focus on developinginfluence functions and local influence to identify influential points/outlyingobservations in spatial data as an alternative approach. The differences be-tween the proposed approach and the existing methods are also investigated.A real data example related Wisconsin tornadoes is given to illustrate theresults.
 1 Introduction 22 Literature Review for Spatial Outliers Detection 42.1 Spatial-Statistic Method . . . . . . . . . . . . . . . . . . . . . 42.2 Scatter-Plot Method . . . . . . . . . . . . . . . . . . . . . . . 43 The Inuence Function 53.1 Theoretical Inuence Function . . . . . . . . . . . . . . . . . . 53.2 Empirical Inuence Function . . . . . . . . . . . . . . . . . . . 53.3 Cut Point Selection . . . . . . . . . . . . . . . . . . . . . . . . 84 Local Inuence 94.1 Construction of the Quasi-likelihood Function . . . . . . . . . 104.2 Cut Point Selection . . . . . . . . . . . . . . . . . . . . . . . . 145 Examples 155.1 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . 155.1.1 Spatial-Statistic . . . . . . . . . . . . . . . . . . . . . . 165.1.2 Scatter-Plot . . . . . . . . . . . . . . . . . . . . . . . . 195.1.3 Empirical Inuence Function for T( ^ F) = ^ . . . . . . . 225.1.4 Empirical Inuence Function for T( ^ F) = ^2 . . . . . . 255.2 A Real Data Example . . . . . . . . . . . . . . . . . . . . . . 286 Conclusion and Discussion 46Reference 49
 [1] Lussky, G. R. (2003) \A Statistical Analysis of Wisconsin TornadoClimatology".[2] Burley, M. W. and Waite, P. J. (1965): Wisconsin Tornadoes. Trans-actions of the Wisconsin Academy of Sciences, Arts and Letters, 54,1-34.[3] SPC, (2002): Tornado Numbers, Deaths, Injuries, and Adjusted Dam-age, 1950-1994. Available 1/10/03 on the world wide web athttp://www.spc.noaa.gov/archive/tornadoes/st-trank.html.[4] Shekhar, S., Lu, C. T. and Zhang, P. (2003) \A Uni ed Approachto Detecting Spatial Outliers". c⃝ 2003 Kluwer Academic Publishers.Manufactured in The Netherlands. GeoInformatica 7:2, 139-166[5] Barnett, V. and Lewis, T. (1994) Outliers in Spatial Data. 3rd edition,John Wiley: New York.[6] Haining, R. P. (1993) Spatial Data Analysis in the Social and Environ-mental Sciences. Cambridge University Press.[7] Hampel, F. R. (1974) The inuence curve and its role in robust esti-mation. Journal of the American Statistical Association; 69: 383-393.[8] Cook, R. D. (1986) Assessment of local inuence. Journal of the RoyalStatistical Society Series B; 48: 133-169.[9] Huang Y., Kao T. L. and Wang T. H. (2007) Inuence functions andlocal inuence in linear discriminant analysis. Computational Statisticsand Data analysis; 51: 3844-3861.[10] Tukey, J. M. (1977) Exploratory Data Analysis, Addison-Wesley.49
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