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

Diserahkan: 19 September 2014/Diterima: 6 Februari 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

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*Pengarang untuk surat-menyurat; email: adzfranc@yahoo.com