Sains Malaysiana 50(7)(2021): 2079-2084

http://doi.org/10.17576/jsm-2021-5007-21

COVRATIO Statistic as A Discrimination Method for Multivariate Normal Distribution

(Statistik COVRATIO sebagai Suatu Kaedah Diskriminasi untuk Taburan Multivariat Normal)

NORLI ANIDA ABDULLAH¹*, AFERA MOHAMAD APANDI², MOHD IQBAL SHAMSUDHEEN³ & YONG ZULINA ZUBAIRI¹

¹Centre for Foundation Studies in Science, University of Malaya, Jalan Universiti, 50603 Kuala Lumpur, Federal Territory, Malaysia

²Instistute of Advanced Studies, University of Malaya, Jalan Universiti, 50603 Kuala Lumpur, Federal Territory, Malaysia

³Department of Statistical Science, University College London, London, United Kingdom

Received: 21 February 2020/Accepted: 19 November 2020

ABSTRACT

The COVRATIO statistic has been used to identify the presence of outlier in data, which is based on deletion approach, where the determinant of covariance matrix for the full dataset excludes i-th row. This study proposes a novel discrimination method for the multivariate normal (MVN) distribution using the idea of COVRATIO statistic, denoted as . The linear discrimination function (LDF) for MVN distribution will be compared to the  statistic. Simulation results showed that the  as discrimination method performs better than the LDF with lower misclassification probabilities in all cases considered. The interest in the discrimination method arose in connection with the study of an application to discriminate the shape of the human maxillary dental arches, thus  statistic may be considered as an alternative.

Keywords: COVRATIO statistic; dental arch; discrimination method; linear discrimination function; multivariate normal distribution

ABSTRAK

Statistik COVRATIO telah digunakan untuk mengenal pasti kehadiran data luar dengan menggunakan kaedah penghapusan, dengan baris i dari penentu matriks kovarians dikeluarkan daripada set data penuh. Kajian ini mencadangkan kaedah diskriminasi baru untuk taburan normal multivariat (MVN) menggunakan idea daripada statistik COVRATIO, yang dikenali sebagai . Fungsi diskriminasi linear (LDF) untuk taburan MVN akan dibandingkan dengan kaedah tersebut. Hasil simulasi menunjukkan bahawa statistik diskriminasi  adalah lebih baik daripada LDF dengan kebarangkalian salah pengelasan yang lebih rendah dalam semua kes yang dipertimbangkan. Kepentingan kaedah diskriminasi timbul dalam kajian membezakan bentuk arkus pergigian maksila manusia dan statistik  ini boleh digunakan sebagai alternatif.

Kata kunci: Arkus pergigian; fungsi diskriminasi linear; kaedah diskriminasi; statistik COVRATIO; taburan multivariat normal

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*Corresponding author; email: norlie@um.edu.my