Research Article
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Year 2023, Volume: 52 Issue: 2, 459 - 486, 31.03.2023
https://doi.org/10.15672/hujms.1122113

Abstract

References

  • [1] H. Abdi and L.J. Williams, Principal component analysis, Wiley Interdiscip. Rev. Comput. Stat. 2 (4), 433-459, 2010.
  • [2] C. Agostinelli, A. Leung, V.J. Yohai and R.H. Zamar, Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination, Test 24 (3), 441-461, 2015.
  • [3] M.H. Ahmad, R. Adnan and N. Adnan, A comparative study on some methods for handling multicollinearity problems, Matematika (Johor) 22 (2), 109-119, 2006.
  • [4] A. Alfons, Package “robustHD: Robust methods for high-dimensional data”, R package version: 0.5.1, 2016.
  • [5] A. Alin, Multicollinearity, Wiley Interdiscip. Rev. Comput. Stat. 2 (3), 370-374, 2010.
  • [6] O.G. Alma, Comparison of robust regression methods in linear regression, Int. J. Contemp. Math. Sciences 6 (9), 409-421, 2011.
  • [7] F. Alqallaf, S. Van Aelst, V.J. Yohai and R.H. Zamar, Propagation of outliers in multivariate data, Ann. Statist. 37 (1), 311-31, 2009.
  • [8] R. Andersen, Modern Methods for Robust Regression, Sage, 2008.
  • [9] A.C. Atkinson, Regression diagnostics, transformations and constructed variables, J. R. Stat. Soc. Ser. B. Stat. Methodol. 44 (1), 1-22, 1982.
  • [10] V. Barnett and T. Lewis, Outliers in Statistical Data, John Wiley & Sons, New York, 1994.
  • [11] D.A. Belsley, E. Kuh and R.E.Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, John Wiley & Sons, 2005.
  • [12] D. Blatná, Outliers in regression, Trutnov 30, 1-6, 2006.
  • [13] B. Campos, F. Paredes, J. Rey, D. Lobo and S. Galvis-Causil, The relationship between the normalized difference vegetation index, rainfall, and potential evapotranspiration in a banana plantation of Venezuela, Sains Tanah 18 (1), 58-64, 2021.
  • [14] S. Chatterjee and A.S. Hadi, Influential observations, high leverage points, and outliers in linear regression, Statist. Sci. 1 (3), 379-393, 1986.
  • [15] S. Chatterjee and A. S. Hadi, Regression Analysis by Example, John Wiley & Sons, 2015.
  • [16] R.D. Cook, Detection of influential observation in linear regression, Technometrics 19 (1), 15-18, 1977.
  • [17] R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman and Hall, New York, 1982.
  • [18] C. Daniel and F.S. Wood, Fitting Equations to Data: Computer Analysis of Multifactor Data, John Wiley & Sons, 1980.
  • [19] M. Denhere and N. Billor, Robust principal component functional logistic regression, Comm. Statist. Simulation Comput. 45 (1), 264-281, 2016.
  • [20] A.K. Dey, M.A. Hossain and K.P. Das, Regression analysis for data containing outliers and high leverage points, Ala. J. Math 39, 1-6, 2015.
  • [21] N.R. Draper and H. Smith, Applied Regression Analysis, John Wiley & Sons, 1998.
  • [22] F.Y. Edgeworth, On observations relating to several quantities, Hermathena 6 (13), 279285, 1887.
  • [23] W.J. Egan and S.L. Morgan, Outlier detection in multivariate analytical chemical data, Anal. Chem. 70 (11), 2372-2379, 1998.
  • [24] S. Engelen, M. Hubert, K.V. Branden and S. Verboven, Robust PCR and Robust PLSR: a comparative study, in: Theory and Applications of Recent Robust Methods, 105-117, Birkhäuser, Basel, 2004.
  • [25] P. Filzmoser, Robust principal component regression, in: Proceedings of the Sixth International Conference on Computer Data Analysis and Modeling, 132137, Minsk, Belarus, 2001.
  • [26] P. Gagnon, M. Bédard and A. Desgagné, An automatic robust Bayesian approach to principal component regression, J. Appl. Stat. 48 (1), 84-104, 2021.
  • [27] D.N. Gujarati, Basic Econometrics, Tata McGraw-Hill Education, New York, 2009.
  • [28] L.C. Hamilton, Statistics with Stata: Version 12, Cengage Learning, 2012.
  • [29] H.V. Henderson and P.F. Velleman, Building multiple regression models interactively, Biometrics 37 (2), 391-411, 1981.
  • [30] D.C. Hoaglin and R.E. Welsch, The hat matrix in regression and ANOVA, Amer. Statist. 32 (1), 17-22, 1987.
  • [31] R.R. Hocking, Developments in linear regression methodology: 19591982, Technometrics 25 (3), 219230, 1983.
  • [32] A.E. Hoerl and R.W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Technometrics 12 (1), 5567, 1970.
  • [33] P.J. Huber, Robust estimation of a location parameter, Ann. Math. Statist. 35, 73- 101, 1964.
  • [34] M. Hubert, P.J. Rousseeuw and W. Van den Bossche, MacroPCA: An all-in-one PCA method allowing for missing values as well as cellwise and rowwise outliers, Technometrics 61 (4), 459-473, 2019.
  • [35] M. Hubert, P.J. Rousseeuw and K.V. Branden, ROBPCA: a new approach to robust principal component analysis, Technometrics 47 (1), 64-79, 2005.
  • [36] M. Hubert and S. Verboven, A robust PCR method for highdimensional regressors, J. Chemom. 17 (89) 438-452, 2003.
  • [37] R.A. Johnson and D.W. Wichern, Applied Multivariate Statistical Analysis, Pearson, London, 2014.
  • [38] I.T. Jolliffe, A note on the use of principal components in regression, J. R. Stat. Soc. Ser. C. Appl. Stat. 31 (3), 300-303, 1982.
  • [39] I.T. Jolliffe, Principal components in regression analysis, in: Principal Component Analysis, 129-155, Springer, New York, 1986.
  • [40] I.T. Jolliffe, Principal component analysis, in: Encyclopedia of Statistics in Behavioural Science, John Wiley & Sons, 2005.
  • [41] H.A. Kiers, Weighted least squares fitting using ordinary least squares algorithms, Psychometrika 62 (2), 251-266, 1997.
  • [42] M.R. Lavery, P. Acharya, S.A. Sivo and L. Xu, Number of predictors and multicollinearity: What are their effects on error and bias in regression?, Comm. Statist. Simulation Comput. 48 (1), 27-38, 2019.
  • [43] G. Li and Z. Chen, Projection-pursuit approach to robust dispersion matrices and principal components: Primary theory and Monte Carlo, J. Amer. Statist. Assoc. 80 (391), 759-66, 1985.
  • [44] D.C. Montgomery and A.E. Peck, Introduction to Linear Regression Analysis, John Wiley & Sons, New York, 1982.
  • [45] E. Montenegro, J. Pitti and O.B. Olivares, Identification of the main subsistence crops of Teribe: a case study based on multivariate techniques, Idesia 39 (3), 83-94, 2021.
  • [46] P.R. Nelson, P.A. Taylor and J.F. MacGregor, Missing data methods in PCA and PLS: Score calculations with incomplete observations, Chemom. Intell. Lab. Syst. 35 (1), 45-65, 1996.
  • [47] J. Neter, M.H. Kutner, C.J. Nachtsheim and W. Wasserman, Applied Linear Statistical Models, McGraw-Hill, New York, 1996.
  • [48] K. Ntotsis and A. Karagrigoriou, The impact of multicollinearity on big data multivariate analysis modeling, in: I. Dimotikalis, A. Karagrigoriou, C. Parpoula and C. Skiadas (ed.) Applied Modeling Techniques and Data Analysis 1: Computational Data Analysis methods and Tools, ISTE, 2021.
  • [49] O.B. Olivares, Determination of the Potential Influence of Soil in the Differentiation of Productivity and in the Classification of Susceptible Areas to Banana Wilt in Venezuela, 89-111, UCOPress, Spain, 2022.
  • [50] O.B. Olivares, M. Araya-Alman and C. Acevedo-Opazo, Relationship between soil properties and banana productivity in the two main cultivation areas in Venezuela, Soil Sci. Plant Nutr. 20 (3), 2512-2524, 2020.
  • [51] O.B. Olivares, J. Calero, J.C. Rey, D. Lobo, B.B. Landa and J.A. Gómez, Correlation of banana productivity levels and soil morphological properties using regularized optimal scaling regression, Catena 208, 105718, 2022.
  • [52] O.B. Olivares and R. Hernández, Application of multivariate techniques in the agricultural lands aptitude in Carabobo, Venezuela, Trop. Subtrop. Agroecosystems 23 (2), 1-12, 2020.
  • [53] O.B. Olivares, J. Pitti and E. Montenegro, Socioeconomic characterization of Bocas del Toro in Panama: an application of multivariate techniques, Rev. Bras. de Gestao e Desenvolv. Reg. 16 (3), 59-71, 2020.
  • [54] S. Paul, Sequential detection of unusual points in regression, J. R. Stat. Soc. Ser. D. (The Statistician) 32 (4), 417-424, 1983.
  • [55] R.K. Paul, Multicollinearity: Causes, effects and remedies, IASRI, New Delhi, 2006.
  • [56] R.J. Pell, Multiple outlier detection for multivariate calibration using robust statistical techniques, Chemom. Intell. Lab. Syst. 52 (1), 87-104, 2000.
  • [57] D. Pena and V. Yohai, A fast procedure for outlier diagnostics in large regression problems, J. Amer. Statist. Assoc. 94 (446), 434-445, 1999.
  • [58] J. Pitti, O.B. Olivares and E. Montenegro, The role of agriculture in the Changuinola District: a case of applied economics in Panama, Trop. Subtrop. Agroecosystems 25 (1), 1-11, 2021.
  • [59] O. Renaud and M.P. Victoria-Feser, A robust coefficient of determination for regression, J. Statist. Plann. Inference 140 (7), 1852-1862, 2010.
  • [60] P.J. Rousseeuw, Least median of squares regression, J. Amer. Statist. Assoc. 79 (388), 871-880, 1984.
  • [61] P.J. Rousseeuw and W.V.D. Bossche, Detecting deviating data cells, Technometrics 60 (2), 135-145, 2018.
  • [62] P.J. Rousseeuw and A.M. Leroy, Robust Regression and Outlier Detection, John Wiley & Sons, 1987.
  • [63] P.J. Rousseeuw and A.M. Leroy, A robust scale estimator based on the shortest half, Stat. Neerl. Statistica 42 (2), 103-116, 1988.
  • [64] P.J. Rousseeuw and B.C. Van Zomeren, Unmasking multivariate outliers and leverage points, J. Amer. Statist. Assoc. 85 (411), 633-639, 1990.
  • [65] P.J. Rousseeuw and V. Yohai, Robust regression by means of S-estimators, in: Robust and Nonlinear Time Series Analysis, 256-272, Springer, New York, 1984.
  • [66] G.A. Seber and A.J. Lee, Linear Regression Analysis, John Wiley & Sons, 2012.
  • [67] S. Serneels and T. Verdonck, Principal component analysis for data containing outliers and missing elements, Comput. Statist. Data Anal. 52 (3), 1712-1727, 2008.
  • [68] N. Shrestha, Detecting multicollinearity in regression analysis, Am. J. Appl. Math. Stat. 8 (2), 39-42, 2020.
  • [69] A.F. Siegel and R.H. Benson, A robust comparison of biological shapes, Biometrics 38 (2), 341-350, 1982.
  • [70] K.K. Singh, A. Patel and C. Sadu, Correlation scaled principal component regression, in: Intelligent Systems Design and Applications, 17th International Conference on Intelligent Systems Design and Applications, 350-356, Springer, 2017.
  • [71] I. Stanimirova, M. Daszykowski and B. Walczak, Dealing with missing values and outliers in principal component analysis, Talanta 72 (1), 172-178, 2007.
  • [72] J.P. Stevens, Outliers and influential data points in regression analysis, Psychol. Bull. 95 (2), 334, 1984.
  • [73] M. Suhail, S. Chand and B.G. Kibria, Quantile based estimation of biasing parameters in ridge regression model, Comm. Statist. Simulation Comput. 49 (10), 2732-2744, 2020.
  • [74] Y. Susanti and H. Pratiwi, M estimation, S estimation, and MM estimation in robust regression, Int. J. Pure Appl. Math. 91 (3), 349-360, 2014.
  • [75] M.A. Ullah and G.R. Pasha, The origin and developments of influence measures in regression, Pakistan J. Statist. 25 (3), 2009.
  • [76] B. Walczak and D.L. Massart, Robust principal components regression as a detection tool for outliers, Chemom. Intell. Lab. Syst. 27 (1), 41-54, 1995.
  • [77] C. Yale and A.B. Forsythe, Winsorized regression, Technometrics 18 (3), 291-300, 1976.
  • [78] M.H. Zhang, Q.S. Xu and D.L. Massart, Robust principal components regression based on principal sensitivity vectors, Chemom. Intell. Lab. Syst. 67 (2), 175-185, 2003.
  • [79] N. Zhao, Q. Xu, M.L. Tang, B. Jiang, Z. Chen and H.Wang, Highdimensional variable screening under multicollinearity, Chemom. Intell. Lab. Syst. 9 (1), 1-11, 2020.

Robust correlation scaled principal component regression

Year 2023, Volume: 52 Issue: 2, 459 - 486, 31.03.2023
https://doi.org/10.15672/hujms.1122113

Abstract

In multiple regression, different techniques are available to deal with the situation where the predictors are large in number, and multicollinearity exists among them. Some of these approaches rely on correlation and others depend on principal components. To cope with the influential observations (outliers, leverage, or both) in the data matrix for regression purposes, two techniques are proposed in this paper. These are Robust Correlation Based Regression (RCBR) and Robust Correlation Scaled Principal Component Regression (RCSPCR). These proposed methods are compared with the existing methods, i.e., traditional Principal Component Regression (PCR), Correlation Scaled Principal Component Regression (CSPCR), and Correlation Based Regression (CBR). Also, Macro (Missingness and cellwise and row-wise outliers) RCSPCR is proposed to cope with the problem of multicollinearity, the high dimensionality of the dataset, outliers, and missing observations simultaneously. The proposed techniques are assessed by considering several simulated scenarios with appropriate levels of contamination. The results indicate that the suggested techniques seem to be more reliable for analyzing the data with missingness and outlyingness. Additionally, real-life data applications are also used to illustrate the performance of the proposed methods.

References

  • [1] H. Abdi and L.J. Williams, Principal component analysis, Wiley Interdiscip. Rev. Comput. Stat. 2 (4), 433-459, 2010.
  • [2] C. Agostinelli, A. Leung, V.J. Yohai and R.H. Zamar, Robust estimation of multivariate location and scatter in the presence of cellwise and casewise contamination, Test 24 (3), 441-461, 2015.
  • [3] M.H. Ahmad, R. Adnan and N. Adnan, A comparative study on some methods for handling multicollinearity problems, Matematika (Johor) 22 (2), 109-119, 2006.
  • [4] A. Alfons, Package “robustHD: Robust methods for high-dimensional data”, R package version: 0.5.1, 2016.
  • [5] A. Alin, Multicollinearity, Wiley Interdiscip. Rev. Comput. Stat. 2 (3), 370-374, 2010.
  • [6] O.G. Alma, Comparison of robust regression methods in linear regression, Int. J. Contemp. Math. Sciences 6 (9), 409-421, 2011.
  • [7] F. Alqallaf, S. Van Aelst, V.J. Yohai and R.H. Zamar, Propagation of outliers in multivariate data, Ann. Statist. 37 (1), 311-31, 2009.
  • [8] R. Andersen, Modern Methods for Robust Regression, Sage, 2008.
  • [9] A.C. Atkinson, Regression diagnostics, transformations and constructed variables, J. R. Stat. Soc. Ser. B. Stat. Methodol. 44 (1), 1-22, 1982.
  • [10] V. Barnett and T. Lewis, Outliers in Statistical Data, John Wiley & Sons, New York, 1994.
  • [11] D.A. Belsley, E. Kuh and R.E.Welsch, Regression Diagnostics: Identifying Influential Data and Sources of Collinearity, John Wiley & Sons, 2005.
  • [12] D. Blatná, Outliers in regression, Trutnov 30, 1-6, 2006.
  • [13] B. Campos, F. Paredes, J. Rey, D. Lobo and S. Galvis-Causil, The relationship between the normalized difference vegetation index, rainfall, and potential evapotranspiration in a banana plantation of Venezuela, Sains Tanah 18 (1), 58-64, 2021.
  • [14] S. Chatterjee and A.S. Hadi, Influential observations, high leverage points, and outliers in linear regression, Statist. Sci. 1 (3), 379-393, 1986.
  • [15] S. Chatterjee and A. S. Hadi, Regression Analysis by Example, John Wiley & Sons, 2015.
  • [16] R.D. Cook, Detection of influential observation in linear regression, Technometrics 19 (1), 15-18, 1977.
  • [17] R.D. Cook and S. Weisberg, Residuals and Influence in Regression, Chapman and Hall, New York, 1982.
  • [18] C. Daniel and F.S. Wood, Fitting Equations to Data: Computer Analysis of Multifactor Data, John Wiley & Sons, 1980.
  • [19] M. Denhere and N. Billor, Robust principal component functional logistic regression, Comm. Statist. Simulation Comput. 45 (1), 264-281, 2016.
  • [20] A.K. Dey, M.A. Hossain and K.P. Das, Regression analysis for data containing outliers and high leverage points, Ala. J. Math 39, 1-6, 2015.
  • [21] N.R. Draper and H. Smith, Applied Regression Analysis, John Wiley & Sons, 1998.
  • [22] F.Y. Edgeworth, On observations relating to several quantities, Hermathena 6 (13), 279285, 1887.
  • [23] W.J. Egan and S.L. Morgan, Outlier detection in multivariate analytical chemical data, Anal. Chem. 70 (11), 2372-2379, 1998.
  • [24] S. Engelen, M. Hubert, K.V. Branden and S. Verboven, Robust PCR and Robust PLSR: a comparative study, in: Theory and Applications of Recent Robust Methods, 105-117, Birkhäuser, Basel, 2004.
  • [25] P. Filzmoser, Robust principal component regression, in: Proceedings of the Sixth International Conference on Computer Data Analysis and Modeling, 132137, Minsk, Belarus, 2001.
  • [26] P. Gagnon, M. Bédard and A. Desgagné, An automatic robust Bayesian approach to principal component regression, J. Appl. Stat. 48 (1), 84-104, 2021.
  • [27] D.N. Gujarati, Basic Econometrics, Tata McGraw-Hill Education, New York, 2009.
  • [28] L.C. Hamilton, Statistics with Stata: Version 12, Cengage Learning, 2012.
  • [29] H.V. Henderson and P.F. Velleman, Building multiple regression models interactively, Biometrics 37 (2), 391-411, 1981.
  • [30] D.C. Hoaglin and R.E. Welsch, The hat matrix in regression and ANOVA, Amer. Statist. 32 (1), 17-22, 1987.
  • [31] R.R. Hocking, Developments in linear regression methodology: 19591982, Technometrics 25 (3), 219230, 1983.
  • [32] A.E. Hoerl and R.W. Kennard, Ridge regression: Biased estimation for nonorthogonal problems, Technometrics 12 (1), 5567, 1970.
  • [33] P.J. Huber, Robust estimation of a location parameter, Ann. Math. Statist. 35, 73- 101, 1964.
  • [34] M. Hubert, P.J. Rousseeuw and W. Van den Bossche, MacroPCA: An all-in-one PCA method allowing for missing values as well as cellwise and rowwise outliers, Technometrics 61 (4), 459-473, 2019.
  • [35] M. Hubert, P.J. Rousseeuw and K.V. Branden, ROBPCA: a new approach to robust principal component analysis, Technometrics 47 (1), 64-79, 2005.
  • [36] M. Hubert and S. Verboven, A robust PCR method for highdimensional regressors, J. Chemom. 17 (89) 438-452, 2003.
  • [37] R.A. Johnson and D.W. Wichern, Applied Multivariate Statistical Analysis, Pearson, London, 2014.
  • [38] I.T. Jolliffe, A note on the use of principal components in regression, J. R. Stat. Soc. Ser. C. Appl. Stat. 31 (3), 300-303, 1982.
  • [39] I.T. Jolliffe, Principal components in regression analysis, in: Principal Component Analysis, 129-155, Springer, New York, 1986.
  • [40] I.T. Jolliffe, Principal component analysis, in: Encyclopedia of Statistics in Behavioural Science, John Wiley & Sons, 2005.
  • [41] H.A. Kiers, Weighted least squares fitting using ordinary least squares algorithms, Psychometrika 62 (2), 251-266, 1997.
  • [42] M.R. Lavery, P. Acharya, S.A. Sivo and L. Xu, Number of predictors and multicollinearity: What are their effects on error and bias in regression?, Comm. Statist. Simulation Comput. 48 (1), 27-38, 2019.
  • [43] G. Li and Z. Chen, Projection-pursuit approach to robust dispersion matrices and principal components: Primary theory and Monte Carlo, J. Amer. Statist. Assoc. 80 (391), 759-66, 1985.
  • [44] D.C. Montgomery and A.E. Peck, Introduction to Linear Regression Analysis, John Wiley & Sons, New York, 1982.
  • [45] E. Montenegro, J. Pitti and O.B. Olivares, Identification of the main subsistence crops of Teribe: a case study based on multivariate techniques, Idesia 39 (3), 83-94, 2021.
  • [46] P.R. Nelson, P.A. Taylor and J.F. MacGregor, Missing data methods in PCA and PLS: Score calculations with incomplete observations, Chemom. Intell. Lab. Syst. 35 (1), 45-65, 1996.
  • [47] J. Neter, M.H. Kutner, C.J. Nachtsheim and W. Wasserman, Applied Linear Statistical Models, McGraw-Hill, New York, 1996.
  • [48] K. Ntotsis and A. Karagrigoriou, The impact of multicollinearity on big data multivariate analysis modeling, in: I. Dimotikalis, A. Karagrigoriou, C. Parpoula and C. Skiadas (ed.) Applied Modeling Techniques and Data Analysis 1: Computational Data Analysis methods and Tools, ISTE, 2021.
  • [49] O.B. Olivares, Determination of the Potential Influence of Soil in the Differentiation of Productivity and in the Classification of Susceptible Areas to Banana Wilt in Venezuela, 89-111, UCOPress, Spain, 2022.
  • [50] O.B. Olivares, M. Araya-Alman and C. Acevedo-Opazo, Relationship between soil properties and banana productivity in the two main cultivation areas in Venezuela, Soil Sci. Plant Nutr. 20 (3), 2512-2524, 2020.
  • [51] O.B. Olivares, J. Calero, J.C. Rey, D. Lobo, B.B. Landa and J.A. Gómez, Correlation of banana productivity levels and soil morphological properties using regularized optimal scaling regression, Catena 208, 105718, 2022.
  • [52] O.B. Olivares and R. Hernández, Application of multivariate techniques in the agricultural lands aptitude in Carabobo, Venezuela, Trop. Subtrop. Agroecosystems 23 (2), 1-12, 2020.
  • [53] O.B. Olivares, J. Pitti and E. Montenegro, Socioeconomic characterization of Bocas del Toro in Panama: an application of multivariate techniques, Rev. Bras. de Gestao e Desenvolv. Reg. 16 (3), 59-71, 2020.
  • [54] S. Paul, Sequential detection of unusual points in regression, J. R. Stat. Soc. Ser. D. (The Statistician) 32 (4), 417-424, 1983.
  • [55] R.K. Paul, Multicollinearity: Causes, effects and remedies, IASRI, New Delhi, 2006.
  • [56] R.J. Pell, Multiple outlier detection for multivariate calibration using robust statistical techniques, Chemom. Intell. Lab. Syst. 52 (1), 87-104, 2000.
  • [57] D. Pena and V. Yohai, A fast procedure for outlier diagnostics in large regression problems, J. Amer. Statist. Assoc. 94 (446), 434-445, 1999.
  • [58] J. Pitti, O.B. Olivares and E. Montenegro, The role of agriculture in the Changuinola District: a case of applied economics in Panama, Trop. Subtrop. Agroecosystems 25 (1), 1-11, 2021.
  • [59] O. Renaud and M.P. Victoria-Feser, A robust coefficient of determination for regression, J. Statist. Plann. Inference 140 (7), 1852-1862, 2010.
  • [60] P.J. Rousseeuw, Least median of squares regression, J. Amer. Statist. Assoc. 79 (388), 871-880, 1984.
  • [61] P.J. Rousseeuw and W.V.D. Bossche, Detecting deviating data cells, Technometrics 60 (2), 135-145, 2018.
  • [62] P.J. Rousseeuw and A.M. Leroy, Robust Regression and Outlier Detection, John Wiley & Sons, 1987.
  • [63] P.J. Rousseeuw and A.M. Leroy, A robust scale estimator based on the shortest half, Stat. Neerl. Statistica 42 (2), 103-116, 1988.
  • [64] P.J. Rousseeuw and B.C. Van Zomeren, Unmasking multivariate outliers and leverage points, J. Amer. Statist. Assoc. 85 (411), 633-639, 1990.
  • [65] P.J. Rousseeuw and V. Yohai, Robust regression by means of S-estimators, in: Robust and Nonlinear Time Series Analysis, 256-272, Springer, New York, 1984.
  • [66] G.A. Seber and A.J. Lee, Linear Regression Analysis, John Wiley & Sons, 2012.
  • [67] S. Serneels and T. Verdonck, Principal component analysis for data containing outliers and missing elements, Comput. Statist. Data Anal. 52 (3), 1712-1727, 2008.
  • [68] N. Shrestha, Detecting multicollinearity in regression analysis, Am. J. Appl. Math. Stat. 8 (2), 39-42, 2020.
  • [69] A.F. Siegel and R.H. Benson, A robust comparison of biological shapes, Biometrics 38 (2), 341-350, 1982.
  • [70] K.K. Singh, A. Patel and C. Sadu, Correlation scaled principal component regression, in: Intelligent Systems Design and Applications, 17th International Conference on Intelligent Systems Design and Applications, 350-356, Springer, 2017.
  • [71] I. Stanimirova, M. Daszykowski and B. Walczak, Dealing with missing values and outliers in principal component analysis, Talanta 72 (1), 172-178, 2007.
  • [72] J.P. Stevens, Outliers and influential data points in regression analysis, Psychol. Bull. 95 (2), 334, 1984.
  • [73] M. Suhail, S. Chand and B.G. Kibria, Quantile based estimation of biasing parameters in ridge regression model, Comm. Statist. Simulation Comput. 49 (10), 2732-2744, 2020.
  • [74] Y. Susanti and H. Pratiwi, M estimation, S estimation, and MM estimation in robust regression, Int. J. Pure Appl. Math. 91 (3), 349-360, 2014.
  • [75] M.A. Ullah and G.R. Pasha, The origin and developments of influence measures in regression, Pakistan J. Statist. 25 (3), 2009.
  • [76] B. Walczak and D.L. Massart, Robust principal components regression as a detection tool for outliers, Chemom. Intell. Lab. Syst. 27 (1), 41-54, 1995.
  • [77] C. Yale and A.B. Forsythe, Winsorized regression, Technometrics 18 (3), 291-300, 1976.
  • [78] M.H. Zhang, Q.S. Xu and D.L. Massart, Robust principal components regression based on principal sensitivity vectors, Chemom. Intell. Lab. Syst. 67 (2), 175-185, 2003.
  • [79] N. Zhao, Q. Xu, M.L. Tang, B. Jiang, Z. Chen and H.Wang, Highdimensional variable screening under multicollinearity, Chemom. Intell. Lab. Syst. 9 (1), 1-11, 2020.
There are 79 citations in total.

Details

Primary Language English
Subjects Statistics
Journal Section Statistics
Authors

Aiman Tahir 0000-0001-5405-8660

Dr. Maryam Ilyas 0000-0002-1662-8340

Publication Date March 31, 2023
Published in Issue Year 2023 Volume: 52 Issue: 2

Cite

APA Tahir, A., & Ilyas, D. M. (2023). Robust correlation scaled principal component regression. Hacettepe Journal of Mathematics and Statistics, 52(2), 459-486. https://doi.org/10.15672/hujms.1122113
AMA Tahir A, Ilyas DM. Robust correlation scaled principal component regression. Hacettepe Journal of Mathematics and Statistics. March 2023;52(2):459-486. doi:10.15672/hujms.1122113
Chicago Tahir, Aiman, and Dr. Maryam Ilyas. “Robust Correlation Scaled Principal Component Regression”. Hacettepe Journal of Mathematics and Statistics 52, no. 2 (March 2023): 459-86. https://doi.org/10.15672/hujms.1122113.
EndNote Tahir A, Ilyas DM (March 1, 2023) Robust correlation scaled principal component regression. Hacettepe Journal of Mathematics and Statistics 52 2 459–486.
IEEE A. Tahir and D. M. Ilyas, “Robust correlation scaled principal component regression”, Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 2, pp. 459–486, 2023, doi: 10.15672/hujms.1122113.
ISNAD Tahir, Aiman - Ilyas, Dr. Maryam. “Robust Correlation Scaled Principal Component Regression”. Hacettepe Journal of Mathematics and Statistics 52/2 (March 2023), 459-486. https://doi.org/10.15672/hujms.1122113.
JAMA Tahir A, Ilyas DM. Robust correlation scaled principal component regression. Hacettepe Journal of Mathematics and Statistics. 2023;52:459–486.
MLA Tahir, Aiman and Dr. Maryam Ilyas. “Robust Correlation Scaled Principal Component Regression”. Hacettepe Journal of Mathematics and Statistics, vol. 52, no. 2, 2023, pp. 459-86, doi:10.15672/hujms.1122113.
Vancouver Tahir A, Ilyas DM. Robust correlation scaled principal component regression. Hacettepe Journal of Mathematics and Statistics. 2023;52(2):459-86.