Simple and fast generalized - M (GM) estimator and its application to real data set
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 po...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Penerbit Universiti Kebangsaan Malaysia
2021
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| Online Access: | http://journalarticle.ukm.my/16924/ http://journalarticle.ukm.my/16924/1/26.pdf |
| _version_ | 1848814178487238656 |
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| author | Habshah Midi, Jayanthi Arasan, Ismaeel, Shelan Saied Mohammed, Mohammed A |
| author_facet | Habshah Midi, Jayanthi Arasan, Ismaeel, Shelan Saied Mohammed, Mohammed A |
| author_sort | Habshah Midi, |
| building | UKM Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T00:29:57Z |
| format | Article |
| id | oai:generic.eprints.org:16924 |
| institution | Universiti Kebangasaan Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T00:29:57Z |
| publishDate | 2021 |
| publisher | Penerbit Universiti Kebangsaan Malaysia |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | oai:generic.eprints.org:169242021-06-28T15:55:29Z http://journalarticle.ukm.my/16924/ Simple and fast generalized - M (GM) estimator and its application to real data set Habshah Midi, Jayanthi Arasan, Ismaeel, Shelan Saied Mohammed, Mohammed A 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. Penerbit Universiti Kebangsaan Malaysia 2021-03 Article PeerReviewed application/pdf en http://journalarticle.ukm.my/16924/1/26.pdf Habshah Midi, and Jayanthi Arasan, and Ismaeel, Shelan Saied and Mohammed, Mohammed A (2021) Simple and fast generalized - M (GM) estimator and its application to real data set. Sains Malaysiana, 50 (3). pp. 859-867. ISSN 0126-6039 https://www.ukm.my/jsm/malay_journals/jilid50bil3_2021/KandunganJilid50Bil3_2021.html |
| spellingShingle | Habshah Midi, Jayanthi Arasan, Ismaeel, Shelan Saied Mohammed, Mohammed A Simple and fast generalized - M (GM) estimator and its application to real data set |
| title | Simple and fast generalized - M (GM) estimator and its application to real data set |
| title_full | Simple and fast generalized - M (GM) estimator and its application to real data set |
| title_fullStr | Simple and fast generalized - M (GM) estimator and its application to real data set |
| title_full_unstemmed | Simple and fast generalized - M (GM) estimator and its application to real data set |
| title_short | Simple and fast generalized - M (GM) estimator and its application to real data set |
| title_sort | simple and fast generalized - m (gm) estimator and its application to real data set |
| url | http://journalarticle.ukm.my/16924/ http://journalarticle.ukm.my/16924/ http://journalarticle.ukm.my/16924/1/26.pdf |