臺灣博碩士論文加值系統

Spatial statistics are mainly aimed to analyze spatial data which are often
correlated in space and are differentiated from typical data. While conduct-
ing a spatial data analysis, observations that are suspicious (e.g. outliers
and/or influential points) will cause problems. Such observations need to
be detected so that appropriate adjustments can be made to the analysis.
Therefore, detection of such influential points in spatial data is essential. In
this thesis, we first review two methods called spatial-statistic and scatter-
plot for the outlier detection in spatial data. Then we focus on developing
influence functions and local influence to identify influential points/outlying
observations 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 the
results.

1 Introduction 2
2 Literature Review for Spatial Outliers Detection 4
2.1 Spatial-Statistic Method . . . . . . . . . . . . . . . . . . . . . 4
2.2 Scatter-Plot Method . . . . . . . . . . . . . . . . . . . . . . . 4
3 The In
uence Function 5
3.1 Theoretical In
uence Function . . . . . . . . . . . . . . . . . . 5
3.2 Empirical In
uence Function . . . . . . . . . . . . . . . . . . . 5
3.3 Cut Point Selection . . . . . . . . . . . . . . . . . . . . . . . . 8
4 Local In
uence 9
4.1 Construction of the Quasi-likelihood Function . . . . . . . . . 10
4.2 Cut Point Selection . . . . . . . . . . . . . . . . . . . . . . . . 14
5 Examples 15
5.1 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . . 15
5.1.1 Spatial-Statistic . . . . . . . . . . . . . . . . . . . . . . 16
5.1.2 Scatter-Plot . . . . . . . . . . . . . . . . . . . . . . . . 19
5.1.3 Empirical In
uence Function for T( ^ F) = ^ . . . . . . . 22
5.1.4 Empirical In
uence Function for T( ^ F) = ^2 . . . . . . 25
5.2 A Real Data Example . . . . . . . . . . . . . . . . . . . . . . 28
6 Conclusion and Discussion 46
Reference 49

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