The Estimation of Bent Line Expectile Regression Model Based on a Smoothing Technique
A bent line expectile regression model can describe the effect of a covariate on the response variable with two different straight lines, which intersect at an unknown change-point. Due to the existence of the change-point, the objective function of the model is not differentiable with respect to th...
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ftmdpi:oai:mdpi.com:/2073-8994/14/7/1320/ 2023-08-20T04:04:58+02:00 The Estimation of Bent Line Expectile Regression Model Based on a Smoothing Technique Jie Liu Jiaqing Chen Yangxin Huang 2022-06-26 application/pdf https://doi.org/10.3390/sym14071320 EN eng Multidisciplinary Digital Publishing Institute https://dx.doi.org/10.3390/sym14071320 https://creativecommons.org/licenses/by/4.0/ Symmetry; Volume 14; Issue 7; Pages: 1320 bent line expectile model change-point smoothing technique estimation Text 2022 ftmdpi https://doi.org/10.3390/sym14071320 2023-08-01T05:30:15Z A bent line expectile regression model can describe the effect of a covariate on the response variable with two different straight lines, which intersect at an unknown change-point. Due to the existence of the change-point, the objective function of the model is not differentiable with respect to the change-point, so it cannot be solved by the method of the traditional linear expectile regression model. For this model, a new estimation method is proposed by a smoothing technique, that is, using Gaussian kernel function to approximate the indicator function in the objective function. It can not only estimate the regression coefficients and change-point location simultaneously, but also have better estimation effect, which compensates for the insufficiency of the previous estimation methods. Under the given regularity conditions, the theoretical proofs of the consistency and asymptotic normality of the proposed estimators are derived. There are two parts of numerical simulations in this paper. Simulation 1 discusses various error distributions at different expectile levels under different conditions, the results show that the mean values of the biases of the estimation method in this paper, and other indicators, are very small, which indicates the robust property of the new method. Simulation 2 considers the symmetric and asymmetric bent lien expectile regression models, the results show that the estimated values of the estimation method in this paper are similar to the true values, which indicates the estimation effect and large sample performance of the proposed method are excellent. In the application research, the method in this paper is applied to the Arctic annual average temperature data and the Nile annual average flow data. The research shows that the standard errors of the estimation method in this paper are very similar to 0, indicating that the parameter estimation accuracy of the new method is very high, and the location of the change-point can be accurately estimated, which further confirms that the ... Text Arctic MDPI Open Access Publishing Arctic Symmetry 14 7 1320 |
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bent line expectile model change-point smoothing technique estimation |
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bent line expectile model change-point smoothing technique estimation Jie Liu Jiaqing Chen Yangxin Huang The Estimation of Bent Line Expectile Regression Model Based on a Smoothing Technique |
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bent line expectile model change-point smoothing technique estimation |
description |
A bent line expectile regression model can describe the effect of a covariate on the response variable with two different straight lines, which intersect at an unknown change-point. Due to the existence of the change-point, the objective function of the model is not differentiable with respect to the change-point, so it cannot be solved by the method of the traditional linear expectile regression model. For this model, a new estimation method is proposed by a smoothing technique, that is, using Gaussian kernel function to approximate the indicator function in the objective function. It can not only estimate the regression coefficients and change-point location simultaneously, but also have better estimation effect, which compensates for the insufficiency of the previous estimation methods. Under the given regularity conditions, the theoretical proofs of the consistency and asymptotic normality of the proposed estimators are derived. There are two parts of numerical simulations in this paper. Simulation 1 discusses various error distributions at different expectile levels under different conditions, the results show that the mean values of the biases of the estimation method in this paper, and other indicators, are very small, which indicates the robust property of the new method. Simulation 2 considers the symmetric and asymmetric bent lien expectile regression models, the results show that the estimated values of the estimation method in this paper are similar to the true values, which indicates the estimation effect and large sample performance of the proposed method are excellent. In the application research, the method in this paper is applied to the Arctic annual average temperature data and the Nile annual average flow data. The research shows that the standard errors of the estimation method in this paper are very similar to 0, indicating that the parameter estimation accuracy of the new method is very high, and the location of the change-point can be accurately estimated, which further confirms that the ... |
format |
Text |
author |
Jie Liu Jiaqing Chen Yangxin Huang |
author_facet |
Jie Liu Jiaqing Chen Yangxin Huang |
author_sort |
Jie Liu |
title |
The Estimation of Bent Line Expectile Regression Model Based on a Smoothing Technique |
title_short |
The Estimation of Bent Line Expectile Regression Model Based on a Smoothing Technique |
title_full |
The Estimation of Bent Line Expectile Regression Model Based on a Smoothing Technique |
title_fullStr |
The Estimation of Bent Line Expectile Regression Model Based on a Smoothing Technique |
title_full_unstemmed |
The Estimation of Bent Line Expectile Regression Model Based on a Smoothing Technique |
title_sort |
estimation of bent line expectile regression model based on a smoothing technique |
publisher |
Multidisciplinary Digital Publishing Institute |
publishDate |
2022 |
url |
https://doi.org/10.3390/sym14071320 |
geographic |
Arctic |
geographic_facet |
Arctic |
genre |
Arctic |
genre_facet |
Arctic |
op_source |
Symmetry; Volume 14; Issue 7; Pages: 1320 |
op_relation |
https://dx.doi.org/10.3390/sym14071320 |
op_rights |
https://creativecommons.org/licenses/by/4.0/ |
op_doi |
https://doi.org/10.3390/sym14071320 |
container_title |
Symmetry |
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14 |
container_issue |
7 |
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1320 |
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1774715395210477568 |