Developing a ridge estimator for the gamma regression model
The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The gamma regression model is a very popular model in the application when the response variable is positively skewed. However, it is known that multicolline...
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| Published in: | Journal of chemometrics Vol. 32; no. 10 |
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| Language: | English |
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| Abstract | The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The gamma regression model is a very popular model in the application when the response variable is positively skewed. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the gamma regression coefficients. To address this problem, a gamma ridge regression model has been proposed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. Our Monte Carlo simulation results and the real data application suggest that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error.
This study deals with the problem of the presence of multicollinearity in regression modeling. The gamma regression model is a very popular model in the application when the response variable is positively skewed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. The simulation results and the real data application reveal that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error. |
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| AbstractList | The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The gamma regression model is a very popular model in the application when the response variable is positively skewed. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the gamma regression coefficients. To address this problem, a gamma ridge regression model has been proposed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. Our Monte Carlo simulation results and the real data application suggest that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error.
This study deals with the problem of the presence of multicollinearity in regression modeling. The gamma regression model is a very popular model in the application when the response variable is positively skewed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. The simulation results and the real data application reveal that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error. Abstract The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The gamma regression model is a very popular model in the application when the response variable is positively skewed. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the gamma regression coefficients. To address this problem, a gamma ridge regression model has been proposed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. Our Monte Carlo simulation results and the real data application suggest that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error. This study deals with the problem of the presence of multicollinearity in regression modeling. The gamma regression model is a very popular model in the application when the response variable is positively skewed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. The simulation results and the real data application reveal that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error. The ridge regression model has been consistently demonstrated to be an attractive shrinkage method to reduce the effects of multicollinearity. The gamma regression model is a very popular model in the application when the response variable is positively skewed. However, it is known that multicollinearity negatively affects the variance of maximum likelihood estimator of the gamma regression coefficients. To address this problem, a gamma ridge regression model has been proposed. In this study, a new estimator is developed by proposing a modification of Jackknife estimator with gamma ridge regression model. Our Monte Carlo simulation results and the real data application suggest that the proposed estimator can bring significant improvement relative to other competitor estimators, in absolute bias and mean squared error. |
| Author | Algamal, Zakariya Yahya |
| Author_xml | – sequence: 1 givenname: Zakariya Yahya orcidid: 0000-0002-0229-7958 surname: Algamal fullname: Algamal, Zakariya Yahya email: zakariya.algamal@uomosul.edu.iq organization: University of Mosul |
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| Cites_doi | 10.1017/CBO9780511755408 10.1080/00949655.2016.1169421 10.1214/aoms/1177729893 10.1080/02664763.2015.1125861 10.1007/s00362-010-0334-5 10.1080/03610918.2014.995815 10.1002/cem.2915 10.1007/s00362-016-0814-3 10.1080/03610928608829223 10.1080/03610926.2012.729640 10.1002/cem.2741 10.1081/SAC-120017499 10.1016/0167-7152(91)90176-R 10.1016/0167-9473(88)90048-5 10.1111/j.2517-6161.1976.tb01588.x 10.1080/03610927508827232 |
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| References | 2015; 5 1950; 21 1991; 11 1986; 13 1986; 15 1970; 12 2009 2008 2008; 3 2016; 57 2012; 53 2003; 32 2014; 43 2017; 31 2015; 29 1988; 6 1977; 19 2015; 43 2016; 86 2018 2017 2016 1976; 38 1975; 4 2016; 45 e_1_2_7_6_1 e_1_2_7_5_1 Uusipaikka E (e_1_2_7_11_1) 2009 e_1_2_7_8_1 e_1_2_7_7_1 Malehi AS (e_1_2_7_4_1) 2015; 5 e_1_2_7_18_1 e_1_2_7_17_1 e_1_2_7_16_1 e_1_2_7_2_1 Türkan S (e_1_2_7_14_1) 2017 e_1_2_7_15_1 e_1_2_7_13_1 e_1_2_7_26_1 Dunder E (e_1_2_7_3_1) 2016 Hoerl AE (e_1_2_7_9_1) 1970; 12 Singh B (e_1_2_7_12_1) 1986; 13 Yıldız N (e_1_2_7_19_1) 2017 e_1_2_7_25_1 Asar Y (e_1_2_7_28_1) 2018 e_1_2_7_24_1 e_1_2_7_23_1 e_1_2_7_21_1 Batah FSM (e_1_2_7_10_1) 2008; 3 Hinkley DV (e_1_2_7_20_1) 1977; 19 Asar Y (e_1_2_7_27_1) 2014; 43 Farebrother R (e_1_2_7_22_1) 1976; 38 |
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| SubjectTerms | Computer simulation Economic models gamma regression model jackknife estimator Maximum likelihood estimators Monte Carlo simulation multicollinearity Regression coefficients Regression models ridge estimator Shrinkage |
| Title | Developing a ridge estimator for the gamma regression model |
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