New Statistical Residuals for Regression Models in the Exponential Family: Characterization, Simulation, Computation, and Applications
Residuals are essential in regression analysis for evaluating model adequacy, validating assumptions, and detecting outliers or influential data. While traditional residuals perform well in linear regression, they face limitations in exponential family models, such as those based on the binomial and...
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| Language: | English |
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MDPI AG
2024-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/12/20/3196 |
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| author | Raydonal Ospina Patrícia L. Espinheira Leilo A. Arias Cleber M. Xavier Víctor Leiva Cecilia Castro |
| author_facet | Raydonal Ospina Patrícia L. Espinheira Leilo A. Arias Cleber M. Xavier Víctor Leiva Cecilia Castro |
| author_sort | Raydonal Ospina |
| collection | DOAJ |
| description | Residuals are essential in regression analysis for evaluating model adequacy, validating assumptions, and detecting outliers or influential data. While traditional residuals perform well in linear regression, they face limitations in exponential family models, such as those based on the binomial and Poisson distributions, due to heteroscedasticity and dependence among observations. This article introduces a novel standardized combined residual for linear and nonlinear regression models within the exponential family. By integrating information from both the mean and dispersion sub-models, the new residual provides a unified diagnostic tool that enhances computational efficiency and eliminates the need for projection matrices. Simulation studies and real-world applications demonstrate its advantages in efficiency and interpretability over traditional residuals. |
| format | Article |
| id | doaj-art-88ec79bf596a4f7e8569aa306092e6cc |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2024-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-88ec79bf596a4f7e8569aa306092e6cc2025-08-20T02:10:56ZengMDPI AGMathematics2227-73902024-10-011220319610.3390/math12203196New Statistical Residuals for Regression Models in the Exponential Family: Characterization, Simulation, Computation, and ApplicationsRaydonal Ospina0Patrícia L. Espinheira1Leilo A. Arias2Cleber M. Xavier3Víctor Leiva4Cecilia Castro5Departamento de Estatística, CASTLab, Universidade Federal de Pernambuco, Recife 50670-901, BrazilDepartamento de Estatística, CASTLab, Universidade Federal de Pernambuco, Recife 50670-901, BrazilDepartamento de Estatística, CASTLab, Universidade Federal de Pernambuco, Recife 50670-901, BrazilDepartamento de Estatística e Ciências Atuariais, Universidade Federal de Sergipe, São Cristóvão 49107-230, BrazilSchool of Industrial Engineering, Pontificia Universidad Católica de Valparaíso, Valparaíso 2362807, ChileCentre of Mathematics, Universidade do Minho, 4710-057 Braga, PortugalResiduals are essential in regression analysis for evaluating model adequacy, validating assumptions, and detecting outliers or influential data. While traditional residuals perform well in linear regression, they face limitations in exponential family models, such as those based on the binomial and Poisson distributions, due to heteroscedasticity and dependence among observations. This article introduces a novel standardized combined residual for linear and nonlinear regression models within the exponential family. By integrating information from both the mean and dispersion sub-models, the new residual provides a unified diagnostic tool that enhances computational efficiency and eliminates the need for projection matrices. Simulation studies and real-world applications demonstrate its advantages in efficiency and interpretability over traditional residuals.https://www.mdpi.com/2227-7390/12/20/3196advanced residual analysiscomputational efficiencyexponential family modelsFisher scoringmean and dispersion integrationmodel adequacy |
| spellingShingle | Raydonal Ospina Patrícia L. Espinheira Leilo A. Arias Cleber M. Xavier Víctor Leiva Cecilia Castro New Statistical Residuals for Regression Models in the Exponential Family: Characterization, Simulation, Computation, and Applications Mathematics advanced residual analysis computational efficiency exponential family models Fisher scoring mean and dispersion integration model adequacy |
| title | New Statistical Residuals for Regression Models in the Exponential Family: Characterization, Simulation, Computation, and Applications |
| title_full | New Statistical Residuals for Regression Models in the Exponential Family: Characterization, Simulation, Computation, and Applications |
| title_fullStr | New Statistical Residuals for Regression Models in the Exponential Family: Characterization, Simulation, Computation, and Applications |
| title_full_unstemmed | New Statistical Residuals for Regression Models in the Exponential Family: Characterization, Simulation, Computation, and Applications |
| title_short | New Statistical Residuals for Regression Models in the Exponential Family: Characterization, Simulation, Computation, and Applications |
| title_sort | new statistical residuals for regression models in the exponential family characterization simulation computation and applications |
| topic | advanced residual analysis computational efficiency exponential family models Fisher scoring mean and dispersion integration model adequacy |
| url | https://www.mdpi.com/2227-7390/12/20/3196 |
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