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STS346 A.H.M. Rahmatullah Imon
classifier to obtain the D set first and then compute GSR and GP as outlined in
equations (5) and (7). It is worth mentioning that the cut-off value for GP is 0.1
based on equation (8). We also present the GP-GSR plot for this data in Figure
3(b). These results clearly show the merit of our proposed method. It can
successfully identify 3 spatial outliers (C, D, and E) and 3 spatial high leverage
points (F, G, H).

4. Discussion and Conclusion
The main objective of our research was to develop a method for the joint
identification of outliers and high leverage points for spatial regression. In
section 2 we develop a new method to identify both of them and propose a
new graphical display called GP-GSR plot to locate both of them in the same
graph. In spatial statistics literature observations with neighborhood instability
are diagnosed as outliers. For this reason we employ our method on the first
order difference of x and y. A numerical example clearly shows the advantage
of using our proposed method. It clearly shows that the proposed method can
successfully identify outliers and high leverage points simultaneously while the
existing methods fail to do so.

References
1. Billor, N., Hadi, A. S., and Velleman, P. F. (2000). BACON: blocked adaptive
computationally efficient outlier nominators, Comput. Statist. Data. Anal.,
34, 279-298.
2. Gray, J. B. (1984). A simple graphic for assessing influence in regression. J.
Statist. Comput. Simul. 24, 121134.
3. Hadi, A. S. (1992). A new measure of overall potential influence in linear
regression. Comput. Statist. Data. Anal. 14, 1-27.
4. Hadi, A.S. and Imon, A.H.M.R. (2018). Identification of multiple outliers in
spatial data, Int. Jour. Statist. Sci., 16, 87-96.
5. Hadi, A. S., Imon, A. H. M. R., and Werner, M. (2009). Detection of outliers,
Wiley Interdisciplinary Reviews: Computational Statistics, 1, 57–70.
6. Imon, A. H. M. R. (2002). Identifying multiple high leverage points in linear
regression, Jour. Statist. Stud., 22, 207–218.
7. Imon, A. H. M. R. (2005). Identifying multiple influential observations in
linear regression, J. App. Stat., 32, 929–946.
8. Shekhar, S., Lu, C., and Zhang, P. (2002). Detecting graph-based spatial
outlier, Intelligent Data Analysis, 6, 451-468.

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