Page 25 - Special Topic Session (STS) - Volume 1

STS346 A.H.M. Rahmatullah Imon

Identification of multiple unusual observations in
spatial regression
1
A.H.M. Rahmatullah Imon , Ali S Hadi 2
1 Department of Mathematical Sciences, Ball State University, USA
2 Department of Mathematics and Actuarial Science, The American University in Cairo,Egypt

Abstract
Traditional outlier detection methods cannot be directly applied to spatial
data because of its global nature. Spatial outlier detection methods
concentrate on discovering neighborhood instabilities [see Shekhar et al.
(2002)]. However, most of the traditional detection methods may not
accurately locate outliers when multiple outliers exist. Robust spatial z test
proposed by Hadi and Imon (2018) has largely resolved this issue. But lots of
unresolved issues exist in spatial regression where likewise linear or
generalized linear models, the entire inferential procedure is generally affected
in the presence of unusual observations called outliers (y-outliers) and high
leverage points (x-outliers) or both. A large body of literature are available now
for the identification of unusual observations in linear and/or generalized
linear regression but this is still an unexplored area in spatial regression. In this
paper we propose a new method for the identification of multiple spatial
outliers and spatial high leverage points based on robust and clustering
algorithms. We also propose a very simple but attractive graphical display to
locate these two types of outliers in the same graph.

Keywords
Spatial outlier; Differencing; Masking; High leverage points; Clustering; GP-
GSR plot.

1. Introduction
Conceptually spatial outliers are very different from classical outliers. A
commonly used definition is that outliers are a minority of observations in a
dataset that have different patterns from that of the majority of observations
in the dataset. The assumption here is that there is a core of at least 50% of
observations in a dataset that are homogeneous (that is, represented by a
common pattern) and the remaining observations (hopefully few) have
patterns that are inconsistent with this common pattern.

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