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Sains Malaysiana 44(7)(2015): 1027–1032 Outlier Detection in a Circular Regression Model (Pengesanan
Terpencil dalam
Model Regresi Berkeliling) ADZHAR RAMBLI1*,
ROSSITA
MOHAMAD
YUNUS1,
IBRAHIM
MOHAMED1
& ABDUL GHAPOR HUSSIN2 1Institute of Mathematical
Sciences, University of Malaya, 59100 Kuala Lumpur, Malaysia 2Centre for Defence Foundation Studies, National Defence
University of Malaysia Kem Sungai Besi, 57000 Kuala Lumpur, Malaysia Received: 19 September
2014/Accepted: 6 February 2015 ABSTRACT Recently, there is strong interest
on the subject of outlier problem in circular data. In this paper,
we focus on detecting outliers in a circular regression model proposed
by Down and Mardia. The basic properties
of the model are available including the exact form of covariance
matrix of the parameters. Hence, we intend to identify outliers
in the model by looking at the effect of the outliers on the covariance
matrix. The method resembles closely the COVRATIO
statistic for the case of linear regression problem. The corresponding
critical values and the performance of the outlier detection procedure
are studied via simulations. For illustration, we apply the procedure
on the wind data set. Keywords: Circular; circular
regression; COVRATIO; influential observation;
outlier ABSTRAK Pada masa ini, terdapat
minat yang mendalam
pada subjek masalah
terpencil dalam
data berkeliling. Dalam
kertas ini,
kami menumpukan untuk mengesan pencilan dalam satu model regresi berkeliling yang dicadangkan oleh Down dan Mardia.
Sifat asas model
yang disediakan termasuk parameter bentuk matriks kovarians yang tepat. Oleh itu, kami berhasrat untuk mengenal pasti pencilan dalam model ini dengan melihat kesan daripada pencilan dalam matriks kovarians. Kaedah ini hampir menyerupai
statistik COVRATIO bagi kes masalah
regresi linear. Nilai kritikal
sepadan dan
prestasi prosedur pengesanan pencilan dikaji melalui simulasi. Untuk ilustrasi, kami menggunakan prosedur set data angin. Kata kunci: Berkeliling;
regresi berkeliling;
COVRATIO; pemerhatian
berpengaruh; terpencil REFERENCES
Abuzaid,
A.H., Hussin, A.G. & Mohamed, I.B.
2013. Detection of outliers in simple regression model using mean circular
error statistic. Journal of Statistical Computation and
Simulation 83(2): 269-277. Abuzaid,
A.H., Mohamed, I.B., Hussin, A.G. &
Rambli, A. 2011. Covratio statistic for simple circular regression model. Chiang
Mai J. Sci. 38(3): 321-330. Barnett,
V. & Lewis, T. 1984. Outliers in Statistical Data.
New York: John Wiley & Sons. Beckman,
R.J. & Cook, R.D. 1983. Outlier..........s. Technometrics
25(2): 119-149. Belsley,
D.A., Kuh, E. & Welsch,
R.E. 1980.
Regression Diagnostic: Identifying Influential Data and Sources
of Collinearity. New York: John Wiley & Sons. Downs,
T.D. & Mardia, K.V. 2002. Circular regression. Biometrika
89(3): 683-697. Hussin,
A.G., Abuzaid, A.H., Zulkifli,
F. & Mohamed, I.B. 2010. Asymptotic covariance and detection of
influential observation in a linear functional relationship model
for circular data with an application to the measurements of winds
directions. SCIENCEASIA 36: 249-253. Hussin,
A.G., Fieller, N.R.J. & Stillman,
E.C. 2004.
Linear regression for circular variables with
application to directional data. Journal of Applied Science
and Technology 8: 1-6. Ibrahim,
S., Rambli, A., Hussin,
A.G. & Mohamed, I. 2013. Outlier detection in
a circular regression model using COVRATIO statistic. Communications
in Statistics- Simulation and Computation 42(10): 2272-2280.
Jammalamadaka, S.R. & Sarma, Y.R. 1993. Circular regression.
In Statistical Sciences and Data Analysis,
edited by Matusita, K. Utrecht: VSP. pp. 109-128. Laycock, P.J. 1975. Optimal
regression: Regression models for directions. Biometrika
62(168): 305-311. Rivest,
L.P. 1997.
A decentred predictor
for circular-circular regression. Biometrika
84(3): 717-726. *Corresponding author; email: adzfranc@yahoo.com
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