Sains Malaysiana 50(3)(2021): 859-867

http://doi.org/10.17576/jsm-2021-5003-26

Simple and Fast Generalized - M (GM) Estimator and Its Application to Real Data Set

(Penganggar Ringkas dan Pantas Teritlak- M dan Kegunaannya ke atas Set Data Sebenar)

HABSHAH MIDI¹*, SHELAN SAIED ISMAEEL², JAYANTHI ARASAN¹ & MOHAMMED A MOHAMMED³

¹Faculty of Science and Institute for Mathematical Research, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor Darul Ehsan, Malaysia

²Department of Mathematics, Faculty of Science, University of Zakho, Iraq

³Al-Dewanyia Technical Institute, AUT, Iraq

Diserahkan: 1 April 2020/Diterima: 9 Ogos 2020

ABSTRACT

It is now evident that some robust methods such as MM-estimator do not address the concept of bounded influence function, which means that their estimates still be affected by outliers in the X directions or high leverage points (HLPs), even though they have high efficiency and high breakdown point (BDP). The Generalized M(GM) estimator, such as the GM6 estimator is put forward with the main aim of making a bound for the influence of HLPs by some weight function. The limitation of GM6 is that it gives lower weight to both bad leverage points (BLPs) and good leverage points (GLPs) which make its efficiency decreases when more GLPs are present in a data set. Moreover, the GM6 takes longer computational time. In this paper, we develop a new version of GM-estimator which is based on simple and fast algorithm. The attractive feature of this method is that it only downs weights BLPs and vertical outliers (VOs) and increases its efficiency. The merit of our proposed GM estimator is studied by simulation study and well-known aircraft data set.

Keywords: DRGP; GM-estimator; high leverage points; index set equality

ABSTRAK

Beberapa kaedah teguh seperti penganggar MM telah dibuktikan tidak dapat menanangi konsep fungsi pengaruh terbatas, yang membawa maksud bahawa penganggar MM masih terjejas dengan titik terpencil dalam arah X atau dikenali sebagai titik tuasan tinggi (HLPs), walaupun ia mempunyai kecekapan dan titik musnah (BDP) yang tinggi. Penganggar -M teritlak (GM), seperti penganggar GM6 dicadangkan dengan tujuan utama membuat batasan kepada pengaruh HLPs dengan fungsi pemberat. Penganggar GM6 mempunyai kekangan dengan memberi pemberat rendah kepada GLPs, yang mengakibatkankecekapan penganggar ini menurun apabila kehadiran HLPs bertambah banyak dalam suatu set data. Tambahan pula, masa pengiraan GM6 terlalu panjang. Dalam kertas ini, kami membangunkan penganggar GM versi baru berdasarkan algoritma yang mudah dan pantas. Sifat menarik yang ada bagi kaedah ini ialah ia hanya menurunkan pemberat bagi BLPs dan VOs dengan ini kecekapannya meningkat. Merit penganggar GM yang kami cadangkan telah dikaji melalui kajian simulasi dan set data kapal terbang yang terkenal.

Kata kunci: DRGP; penganggar GM; set indek kesamaan; titik musnah tinggi

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*Pengarang untuk surat-menyurat; email: habshah@upm.edu.my