Uncertain Gompertz regression model with imprecise observations

Hu, Zeyu; Gao, Jinwu

doi:10.1007/s00500-018-3611-1

Cited by 27 publications

(7 citation statements)

References 8 publications

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“…Yao and Liu ( 2018 ) proposed a least square method for regression by characterizing imprecise observations as uncertain variables. Then several other regression models (Hu and Gao 2020 ; Fang and Hong 2020 ; Zhang et al 2020 ) were further studied, and parameter estimation methods (Liu and Yang 2020 ; Chen 2020 ; Li et al 2022 ) were discussed. In the meantime, confidence interval (Lio and Liu 2018 ), and hypothesis test (Lio and Liu 2020 ) for uncertain statistic were also introduced.…”

Section: Introductionmentioning

confidence: 99%

An uncertain support vector machine based on soft margin method

Qin

Liu

2022

J Ambient Intell Human Comput

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Traditional support vector machines (SVMs) play an important role in the classification of precise data. However, due to various reasons, available data are sometimes imprecise. In this paper, uncertain variables are adopted to describe the imprecise data, and an uncertain support vector machine (USVM) is built for linearly -nonseparable sets based on soft margin method, where a penalty coefficient is utilized as the trade-off between the maximum margin and the sum of slack variables. Then the equivalent crisp model is derived based on the inverse uncertainty distributions. Numerical experiments are designed to illustrate the application of the soft margin USVM. Finally, metrics, such as accuracy, precision, and recall are used to evaluate the robustness of the proposed model.

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Section: Introductionmentioning

confidence: 99%

An uncertain support vector machine based on soft margin method

Qin

Liu

2022

J Ambient Intell Human Comput

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“…For instance, an uncertain linear regression model is established based on uncertainty theory [8], Yao and Liu [9] proposed least-squares estimation, Song and Fu [10] introduced a least squares method to estimate unknown parameters of uncertain multivariable linear regression, and Lio and Liu [11,12] suggested the residuals and confidence interval then came up with the uncertain MLE estimation. Meanwhile, the residual analysis of uncertain Gompertz regression model was provided by Hu and Gao [13]. Liu et al [14] presented a k-fold cross-validation method for the model selection of inaccurate observations.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Analysis of the Uncertain Alternative Box-Cox Regression Model

2021

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The asymmetry of residuals about the origin is a severe issue in estimating a Box-Cox transformed model. In the framework of uncertainty theory, there are such theoretical issues regarding the least-squares estimation (LSE) and maximum likelihood estimation (MLE) of the linear models after the Box-Cox transformation on the response variables. Heretofore, only weighting methods for least-squares analysis have been available. This article proposes an uncertain alternative Box-Cox model to alleviate the asymmetry of residuals and avoid λ tending to negative infinity for uncertain LSE or uncertain MLE. Such symmetry of residuals about the origin is reasonable in applications of experts’ experimental data. The parameter estimation method was given via a theorem, and the performance of our model was supported via numerical simulations. According to the numerical simulations, our proposed ‘alternative Box-Cox model’ can overcome the problems of a grossly underestimated lambda and the asymmetry of residuals. The estimated residuals neither deviated from zero nor changed unevenly, in clear contrast to the LSE and MLE for the uncertain Box-Cox model downward biased residuals. Thus, though the LSE and MLE are not applicable on the uncertain Box-Cox model, they fit the uncertain alternative Box-Cox model. Compared with the uncertain Box-Cox model, the issue of a systematically underestimated λ is not likely to occur in our uncertain alternative Box-Cox model. Both the LSE and MLE can be used directly without constructing a weighted estimation method, offering better performance in the asymmetry of residuals.

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“…Uncertain regression analysis has also been successfully extended in many directions, including uncertain multivariable regression model [9], multivariate regression analysis [10,11], nonparametric regression analysis [12], and so on. In addition, some other uncertain regression models were analysed, such as the uncertain Chapman-Richards growth model [13], the uncertain Verhulst-Pearl model [14], the uncertain Gompertz regression model [15], the uncertain revised regression model [16], and so on.…”

Section: Introductionmentioning

confidence: 99%

Analysis and Prediction for Confirmed COVID-19 Cases in Czech Republic with Uncertain Logistic Growth Model

Ding

Liu

2021

Symmetry

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This paper presents an uncertain logistic growth model to analyse and predict the evolution of the cumulative number of COVID-19 infection in Czech Republic. Some fundamental knowledge about the uncertain regression analysis are reviewed firstly. Stochastic regression analysis is invalid to model cumulative number of confirmed COVID-19 cases in Czech Republic, by considering the disturbance term as random variables, because that the normality test and the identical distribution test of residuals are not passed, and the residual plot does not look like a null plot in the sense of probability theory. In this case, the uncertain logistic growth model is applied by characterizing the disturbance term as uncertain variables. Then parameter estimation, residual analysis, the forecast value and confidence interval are studied. Additionally, the uncertain hypothesis test is proposed to evaluate the appropriateness of the fitted logistic growth model and estimated disturbance term. The analysis and prediction for the cumulative number of COVID-19 infection in Czech Republic can propose theoretical support for the disease control and prevention. Due to the symmetry and similarity of epidemic transmission, other regions of COVID-19 infections, or other diseases can be disposed in a similar theory and method.

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Uncertain Gompertz regression model with imprecise observations

Cited by 27 publications

References 8 publications

An uncertain support vector machine based on soft margin method

An uncertain support vector machine based on soft margin method

Symmetry Analysis of the Uncertain Alternative Box-Cox Regression Model

Analysis and Prediction for Confirmed COVID-19 Cases in Czech Republic with Uncertain Logistic Growth Model

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