Method of moments for estimating uncertainty distributions

Wang, Qianqian; Zhi-qiang, Peng

doi:10.1186/2195-5468-2-5

Cited by 73 publications

(50 citation statements)

References 10 publications

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“…Since the predictions of security returns are mainly made based on experienced experts' estimations in real life [24], Wang et al [31] and Huang and Qiao [24] applied the Delphi method to estimate the uncertainty distribution of uncertain variables. The Delphi method was proposed by Linstone and Turoff [32] in the 1950s and this method is also applicable to other securities [24].…”

Section: Experts' Estimated Values Of Expected Return and Standard Dementioning

confidence: 99%

A Risk-Free Protection Index Model for Portfolio Selection with Entropy Constraint under an Uncertainty Framework

Gao

Huicheng

2017

Entropy

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This paper aims to develop a risk-free protection index model for portfolio selection based on the uncertain theory. First, the returns of risk assets are assumed as uncertain variables and subject to reputable experts' evaluations. Second, under this assumption, combining with the risk-free interest rate we define a risk-free protection index (RFPI), which can measure the protection degree when the loss of risk assets happens. Third, note that the proportion entropy serves as a complementary means to reduce the risk by the preset diversification requirement. We put forward a risk-free protection index model with an entropy constraint under an uncertainty framework by applying the RFPI, Huang's risk index model (RIM), and mean-variance-entropy model (MVEM). Furthermore, to solve our portfolio model, an algorithm is given to estimate the uncertain expected return and standard deviation of different risk assets by applying the Delphi method. Finally, an example is provided to show that the risk-free protection index model performs better than the traditional MVEM and RIM.

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Section: Experts' Estimated Values Of Expected Return and Standard Dementioning

confidence: 99%

A Risk-Free Protection Index Model for Portfolio Selection with Entropy Constraint under an Uncertainty Framework

Gao

Huicheng

2017

Entropy

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“…A method based on the principle of least squares was suggested by Liu (2007) for estimating the parameters of uncertainty distribution. Later, a new method namely method of moments was suggested by Wang and Peng (2014). Besides, a statistical method called uncertain hypothesis testing was suggested by in order to test whether two uncertainty distributions are equal.…”

Section: Introductionmentioning

confidence: 99%

A Regression Model Based on Uncertain Set

Li¹,

Wang²,

Sampath³

et al. 2017

ABR

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Traditional regression analysis is a method of statistical data analysis based on probability theory. Regression models play crucial roles in various branches of statistics including design of experiments, econometrics etc. In regression models, the dependent variable is assumed to be of stochastic nature where randomness enters via errors. Further, the independent variables are assumed to be of deterministic nature. The regression coefficients which explain the interdependency between the variables are assumed to be crisp quantities. Whenever, difficulty arises in expressing the values taken by the dependent variable in terms of crisp quantities, traditional regression models become irrelevant. This paper provides a framework for dealing with such situations on using the notion of uncertain sets of various forms. In this paper, a solution for this problem obtained via linear programming technique is introduced along with an illustrative example.

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“…Besides, Liu [13] introduced the principle of least squares method for uncertain statistics. Furthermore, Wang and Peng [21] proposed the method of moments. Uncertain risk analysis and uncertain reliability analysis were discussed by Liu [12].…”

Section: Introductionmentioning

confidence: 99%

Uncertain Multiobjective Programming and Uncertain Goal Programming

Liu

Chen

2015

J. Uncertain. Anal. Appl.

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Multiobjective programming, known as multi-criteria or multi-attribute optimization, is the process of simultaneously optimizing two or more conflicting objectives. This paper aims to provide a new multiobjective programming named uncertain multiobjective programming that is a type of multiobjective programming involving uncertain variables. Some mathematical properties are also explored. Besides, uncertain goal programming is introduced as a compromise method for solving the uncertain multiobjective programming models. Both the uncertain multiobjective programming model and the uncertain goal programming model are transformed to crisp programming models with the help of the operational law of uncertain variables via inverse uncertainty distributions.

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Method of moments for estimating uncertainty distributions

Cited by 73 publications

References 10 publications

A Risk-Free Protection Index Model for Portfolio Selection with Entropy Constraint under an Uncertainty Framework

A Risk-Free Protection Index Model for Portfolio Selection with Entropy Constraint under an Uncertainty Framework

A Regression Model Based on Uncertain Set

Uncertain Multiobjective Programming and Uncertain Goal Programming

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