Sains Malaysiana 47(6)(2018): 1319–1326

http://dx.doi.org/10.17576/jsm-2018-4706-29

A New Discordancy Test on a Regression for Cylindrical Data

(Ujian Ketakselanjaran Terbaru ke atas Regresi untuk Data Silinder)

NURUL HIDAYAH SADIKON, ADRIANA IRAWATI NUR IBRAHIM*, IBRAHIM MOHAMED & DHARINI PATHMANATHAN

Institute of Mathematical Sciences, University of Malaya, 50603 Kuala Lumpur, Malaysia

Diserahkan: 12 Mei 2017/Diterima: 6 Februari 2018

ABSTRACT

A cylindrical data set consists of circular and linear variables. We focus on developing an outlier detection procedure for cylindrical regression model proposed by Johnson and Wehrly (1978) based on the k-nearest neighbour approach. The procedure is applied based on the residuals where the distance between two residuals is measured by the Euclidean distance. This procedure can be used to detect single or multiple outliers. Cut-off points of the test statistic are generated and its performance is then evaluated via simulation. For illustration, we apply the test on the wind data set obtained from the Malaysian Meteorological Department.

Keywords: Circular-linear; cylindrical data; k-nearest neighbour's distance; outlier

ABSTRAK

Data silinder adalah data yang mengandungi pemboleh ubah bulatan dan linear. Kami memberi tumpuan kepada pembangunan prosedur pengecaman nilai tersisih untuk model regresi silinder yang dicadangkan oleh Johnson dan Wehrly (1978) dengan menggunakan pendekatan jiran k-terdekat. Prosedur tersebut adalah berdasarkan nilai-nilai reja dengan jarak di antara dua reja diukur menggunakan jarak Euclidean. Prosedur ini boleh digunakan untuk mengesan nilai tersisih tunggal atau berbilang. Titik potongan untuk statistik ujian dijana dan prestasi bagi ujian tersebut dikaji secara simulasi. Untuk ilustrasi, kami menggunakan set data angin yang diperoleh daripada Jabatan Meteorologi Malaysia.

Kata kunci: Bulatan-linear; data silinder; jarak jiran k-terdekat; nilai tersisih

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*Pengarang untuk surat-menyurat; email: adrianaibrahim@um.edu.my