Sains Malaysiana 42(6)(2013): 869–874
Detection
of Outliers in the Complex Linear Regression Model
(Pengesanan Nilai Tersisih dalam Model Regresi Linear Kompleks)
Abdul Ghapor Hussin*
Faculty of Science and Defence Technology, National Defence University of Malaysia
57000 Kuala Lumpur, Malaysia
Ali H M Abu Zaid
Faculty of Science, Al-Azhar University-Gaza, Palestine
Adriana Irawaty Nur Ibrahim & Adzhar Rambli
Institute of Mathematical Sciences,
University of Malaya. 50603 Kuala Lumpur
Malaysia
Diserahkan: 10 Ogos 2012/Diteirma:
20 Oktober 2012
ABSTRACT
The existence of outliers in any type of data affects the
estimation of models’ parameters. To date there are very few literatures on
outlier detection tests in circular regression and it motivated us to propose
simple techniques to detect any outliers. This paper considered the complex
linear regression model to fit circular data. The complex residuals of complex
linear regression model were expressed in two different ways in order to detect
possible outliers. Numerical example of the wind direction data was used to
illustrate the efficiency of proposed procedures. The results were very much in
agreement with the results obtained by using the circular residuals of the
simple regression model for circular variables.
Keywords: Circular variables; complex linear regression model;
outlier
ABSTRAK
Kewujudan nilai tersisih dalam mana-mana jenis data mempengaruhi anggaran parameter
model. Sehingga kini sangat sedikit kajian dijalankan mengenai ujian pengesanan nilai tersisih dalam regresi bulatan dan ini mendorong kami untuk mencadangkan teknik mudah untuk mengesan sebarang nilai tersisih. Kajian ini mempertimbangkan penggunaan model regresi linear kompleks untuk menyuaikan data bulatan. Reja kompleks daripada model regresi linear kompleks dinyatakan dalam dua cara yang berbeza untuk mengesan nilai tersisih yang mungkin. Contoh berangka iaitu data arah angin digunakan untuk menggambarkan kecekapan prosedur yang dicadangkan. Keputusan yang diperoleh amat bersetuju dengan keputusan yang diperoleh dengan menggunakan reja bulatan daripada model regresi mudah untuk pemboleh ubah bulatan.
Kata kunci: Model regresi linear kompleks; nilai tersisih; pemboleh ubah bulatan
RUJUKAN
Abuzaid, A.H., Hussin, A.G. & Mohamed, I.B.
2008. Identifying single outlier in linear circular regression model based on
circular distance. Journal of Applied Probability and Statistics 3(1):
107-117.
Abuzaid, A.H., Mohamed, I.B. & Hussin,
A.G. 2009. A new test of discordancy in circular data. Communications in Statistics - Simulation and Computation 38(4):
682-691.
Abuzaid, A.H., Mohamed, I., Hussin, A.G.
& Rambli, A. 2011. COVRATIO
statistic for simple circular regression model. Chiang Mai
International Journal of Science and Technology 38(3): 321-330.
Abuzaid, A.H., Mohamed, I. & Hussin, A.G. 2012a. Circular Boxplot. Computational Statistics 27(3): 381-392.
Abuzaid, A.H., Hussin,
A.G., Rambli, A. & Mohamed, I.B. 2012b. Statistics for a new test of discordance
in circular data. Communication in Statistics: Simulation and
Computation 41(10): 1882-1890.
Collett, D. 1980. Outliers in circular data. Applied
Statistics 29(1): 50-57.
Dobson, A.J. 1978. Simple approximation
for the concentration parameters for the von Mises concentration parameter. Applied Statistics 27: 345-347.
Downs, T.D. & Mardia, K.V.
2002. Circular regression. Biometrika 89(3):
683-697.
Fisher, N.I. & Lee, A.J. 1992. Regression models for an
angular response. Biometrics 48: 665-677.
Gould, A.L. 1969. A regression technique
for angular response. Biometrics 25: 683-700.
Hussin, A.G., Abdullah, N.A. & Mohamed, I. 2010. A complex linear regression model. Sains Malaysiana39(3): 491-494.
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 & Technology 8(1 & 2): 1-6.
Kato, S., Shimizu, K. & Shieh, G.S. 2008. A circular-circular regression model. Statistica Sinica18: 633-643.
Laycock, P.J. 1975. Optimal design: Regression model for
directions. Biometrika 62: 305-311.
Mardia, K.V. 1972. Statistics of Directional
Data. London: Academic Press.
Rambli, A., Ibrahim, S., Abdullah, M.I.,
Mohamed, I. & Hussin, A.G. 2012. On discordance test for the wrapped
normal data. Sains Malaysiana41(6): 769-778.
*Pengarang untuk surat-menyurat; email: abdulghapor@gmail.com
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