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

Received: 10 August 2012/Accepted: 20 October 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

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*Corresponding author; email: abdulghapor@gmail.com