Outlier Detection Method in Linear Regression Based on Sum of Arithmetic Progression
We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio ( R ) of the sum of the minimum and the maximum elements and the sum of all elements...
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| Published in: | TheScientificWorld Vol. 2014; no. 2014; pp. 1 - 12 |
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| Main Authors: | , , , |
| Format: | Journal Article |
| Language: | English |
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Cairo, Egypt
Hindawi Publishing Corporation
01.01.2014
John Wiley & Sons, Inc Wiley |
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| ISSN: | 2356-6140, 1537-744X, 1537-744X |
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| Abstract | We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio ( R ) of the sum of the minimum and the maximum elements and the sum of all elements is always 2 / n : ( 0,1 ] . R ≠ 2 / n always implies the existence of outliers. Usually, R < 2 / n implies that the minimum is an outlier, and R > 2 / n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of ± 1.0 e - 2 to ± 1.0 e + 2 from the correct value. |
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| AbstractList | We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio (R) of the sum of the minimum and the maximum elements and the sum of all elements is always 2/n : (0,1]. R ≠ 2/n always implies the existence of outliers. Usually, R < 2/n implies that the minimum is an outlier, and R > 2/n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of ±1.0e − 2 to ±1.0e + 2 from the correct value. We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio ( R ) of the sum of the minimum and the maximum elements and the sum of all elements is always 2 / n : ( 0,1 ] . R ...0; 2 / n always implies the existence of outliers. Usually, R < 2 / n implies that the minimum is an outlier, and R > 2 / n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of ± 1.0 e - 2 to ± 1.0 e + 2 from the correct value. We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio ( R ) of the sum of the minimum and the maximum elements and the sum of all elements is always 2 / n : ( 0,1 ] . R ≠ 2 / n always implies the existence of outliers. Usually, R < 2 / n implies that the minimum is an outlier, and R > 2 / n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of ± 1.0 e - 2 to ± 1.0 e + 2 from the correct value. We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio (R) of the sum of the minimum and the maximum elements and the sum of all elements is always 2/n : (0,1]. R [not equal to] 2/n always implies the existence of outliers. Usually, R < 2/n implies that the minimum is an outlier, and R > 2/n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of [+ or -] 1.0e - 2 to [+ or -] 1.0e + 2 from the correct value. We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio (R) of the sum of the minimum and the maximum elements and the sum of all elements is always 2/n:(0,1]. R≠2/n always implies the existence of outliers. Usually, R<2/n implies that the minimum is an outlier, and R>2/n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of ±1.0e-2 to ±1.0e+2 from the correct value. We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio (R) of the sum of the minimum and the maximum elements and the sum of all elements is always 2/n : (0,1]. R ≠ 2/n always implies the existence of outliers. Usually, R < 2/n implies that the minimum is an outlier, and R > 2/n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of ±1.0e - 2 to ±1.0e + 2 from the correct value. We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio (R) of the sum of the minimum and the maximum elements and the sum of all elements is always 2/n : (0,1]. R ≠ 2/n always implies the existence of outliers. Usually, R < 2/n implies that the minimum is an outlier, and R > 2/n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of ±1.0e - 2 to ±1.0e + 2 from the correct value.We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio (R) of the sum of the minimum and the maximum elements and the sum of all elements is always 2/n : (0,1]. R ≠ 2/n always implies the existence of outliers. Usually, R < 2/n implies that the minimum is an outlier, and R > 2/n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of ±1.0e - 2 to ±1.0e + 2 from the correct value. We introduce a new nonparametric outlier detection method for linear series, which requires no missing or removed data imputation. For an arithmetic progression (a series without outliers) with n elements, the ratio ( R ) of the sum of the minimum and the maximum elements and the sum of all elements is always 2 / n : ( 0,1 ] . R ≠ 2 / n always implies the existence of outliers. Usually, R < 2 / n implies that the minimum is an outlier, and R > 2 / n implies that the maximum is an outlier. Based upon this, we derived a new method for identifying significant and nonsignificant outliers, separately. Two different techniques were used to manage missing data and removed outliers: (1) recalculate the terms after (or before) the removed or missing element while maintaining the initial angle in relation to a certain point or (2) transform data into a constant value, which is not affected by missing or removed elements. With a reference element, which was not an outlier, the method detected all outliers from data sets with 6 to 1000 elements containing 50% outliers which deviated by a factor of ± 1.0 e - 2 to ± 1.0 e + 2 from the correct value. |
| Audience | Academic |
| Author | Effenberger, M. Adikaram, K. K. L. B. Hussein, M. A. Becker, T. |
| AuthorAffiliation | 1 Group Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, Germany 2 Institut für Landtechnik und Tierhaltung, Vöttinger Straße 36, 85354 Freising, Germany 3 Computer Unit, Faculty of Agriculture, University of Ruhuna, Mapalana, 81100 Kamburupitiya, Sri Lanka |
| AuthorAffiliation_xml | – name: 1 Group Bio-Process Analysis Technology, Technische Universität München, Weihenstephaner Steig 20, 85354 Freising, Germany – name: 3 Computer Unit, Faculty of Agriculture, University of Ruhuna, Mapalana, 81100 Kamburupitiya, Sri Lanka – name: 2 Institut für Landtechnik und Tierhaltung, Vöttinger Straße 36, 85354 Freising, Germany |
| Author_xml | – sequence: 1 fullname: Becker, T. – sequence: 2 fullname: Effenberger, M. – sequence: 3 fullname: Hussein, M. A. – sequence: 4 fullname: Adikaram, K. K. L. B. |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/25121139$$D View this record in MEDLINE/PubMed |
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| CitedBy_id | crossref_primary_10_1002_cem_3143 crossref_primary_10_1016_j_schres_2019_08_013 crossref_primary_10_1007_s11356_023_27176_x crossref_primary_10_1016_j_molliq_2017_04_109 crossref_primary_10_1016_j_epsr_2020_106885 crossref_primary_10_1080_03610918_2021_2007400 crossref_primary_10_1186_s13640_019_0416_9 |
| Cites_doi | 10.1016/0734-189X(83)90047-6 10.1155/2013/720392 10.1155/2010/513810 10.1155/2014/796279 10.1016/j.sigpro.2010.03.014 10.1080/19466315.2013.847383 10.1023/B:AIRE.0000045502.10941.a9 10.1080/00401706.1969.10490657 10.2307/1268354 10.1016/j.acha.2010.11.007 10.1080/00401706.1981.10486239 10.1007/978-3-642-23881-9_50 10.1007/11731139_66 10.1016/j.compchemeng.2004.01.009 10.1076/edre.7.4.353.8937 10.1198/jasa.2009.tm08163 10.1016/j.jsp.2009.10.001 10.1198/jbes.2009.07161 10.1037//1082-989X.7.2.147 10.1155/2014/746451 |
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| Copyright | Copyright © 2014 K. K. L. B. Adikaram et al. COPYRIGHT 2014 John Wiley & Sons, Inc. Copyright © 2014 K. K. L. B. Adikaram et al. K. K. L. B. Adikaram et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Copyright © 2014 K. K. L. B. Adikaram et al. 2014 |
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Zaïane O. R. Foss A. Wu J. Ng W.-K. Kitsuregawa M. Li J. Chang K. A nonparametric outlier detection for effectively discovering top-N outliers from engineering data Advances in Knowledge Discovery and Data Mining 2006 3918 Berlin, Germany Springer 557 566 Lecture Notes in Computer Science 2-s2.0-33745800069 – volume: 5 start-page: 1 issue: 1–4 year: 2011 end-page: 13 ident: 17 article-title: Review of the methods for handling missing data in longitudinal data analysis – volume: 17 start-page: 221 issue: 2 year: 1975 end-page: 227 ident: 27 article-title: On the detection of many outliers – reference: Williams G. Baxter R. He H. Hawkins S. Gu L. A comparative study of RNN for outlier detection in data mining Proceedings of the IEEE International Conference on Data Mining (ICDM '02) December 2002 709 712 2-s2.0-27144452309 – reference: Jin W. Tung A. K. H. Han J. 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| SubjectTerms | Algorithms Biogas Colleges & universities Data Interpretation, Statistical Electronic data processing Genetic algorithms Linear Models Linear models (Statistics) Linear regression models Mathematical Concepts Methods Numerical Analysis, Computer-Assisted Regression analysis |
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| Title | Outlier Detection Method in Linear Regression Based on Sum of Arithmetic Progression |
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