scholarly journals Dependence uncertainty bounds for the energy score and the multivariate Gini mean difference

2020 ◽  
Vol 8 (1) ◽  
pp. 239-253
Author(s):  
Carole Bernard ◽  
Alfred Müller
Keyword(s):  
Multivariate Statistics ◽  
Mean Difference ◽  
Dependence Structure ◽  
Spherically Symmetric ◽  
Probabilistic Forecasting ◽  
Gini Mean Difference ◽  
Energy Score ◽  
Energy Distance ◽  
Symmetric Copula

AbstractThe energy distance and energy scores became important tools in multivariate statistics and multivariate probabilistic forecasting in recent years. They are both based on the expected distance of two independent samples. In this paper we study dependence uncertainty bounds for these quantities under the assumption that we know the marginals but do not know the dependence structure. We find some interesting sharp analytic bounds, where one of them is obtained for an unusual spherically symmetric copula. These results should help to better understand the sensitivity of these measures to misspecifications in the copula.

The Use of Gini Mean Difference for Monitoring Process Capability

2015 ◽  
Vol 4 (1) ◽  
pp. 45-66
Author(s):  
Kalpana Mahajan ◽  
Sangeeta Arora ◽  
Priyanka Vashista
Keyword(s):  
Process Capability ◽  
Mean Difference ◽  
Gini Mean Difference ◽  
Monitoring Process

Notes on Cumulative Entropy as a Risk Measure

2019 ◽  
Vol 34 (1) ◽  
pp. 1-7
Author(s):  
Saeid Tahmasebi ◽  
Hojat Parsa
Keyword(s):  
Standard Deviation ◽  
Stock Market ◽  
Risk Measure ◽  
Oecd Countries ◽  
Mean Difference ◽  
Empirical Approach ◽  
Differential Entropy ◽  
Gini Mean Difference ◽  
Cumulative Entropy

Abstract Di Crescenzo and Longobardi [Di Crescenzo and Longobardi, On cumulative entropies, J. Statist. Plann. Inference 139 2009, 12, 4072–4087] proposed the cumulative entropy (CE) as an alternative to the differential entropy. They presented an estimator of CE using empirical approach. In this paper, we consider a risk measure based on CE and compare it with the standard deviation and the Gini mean difference for some distributions. We also make empirical comparisons of these measures using samples from stock market in members of the Organization for Economic Co-operation and Development (OECD) countries.

scholarly journals The energy distance for ensemble and scenario reduction

2021 ◽  
Vol 379 (2202) ◽  
pp. 20190431 ◽  
Author(s):  
Florian Ziel
Keyword(s):  
Power Systems ◽  
Real Data ◽  
Wasserstein Distance ◽  
Generative Adversarial Networks ◽  
Probabilistic Forecasting ◽  
Multivariate Distributions ◽  
Scenario Reduction ◽  
Stochastic Programs ◽  
Reduction Techniques ◽  
Energy Distance

Scenario reduction techniques are widely applied for solving sophisticated dynamic and stochastic programs, especially in energy and power systems, but are also used in probabilistic forecasting, clustering and estimating generative adversarial networks. We propose a new method for ensemble and scenario reduction based on the energy distance which is a special case of the maximum mean discrepancy. We discuss the choice of energy distance in detail, especially in comparison to the popular Wasserstein distance which is dominating the scenario reduction literature. The energy distance is a metric between probability measures that allows for powerful tests for equality of arbitrary multivariate distributions or independence. Thanks to the latter, it is a suitable candidate for ensemble and scenario reduction problems. The theoretical properties and considered examples indicate clearly that the reduced scenario sets tend to exhibit better statistical properties for the energy distance than a corresponding reduction with respect to the Wasserstein distance. We show applications to a Bernoulli random walk and two real data-based examples for electricity demand profiles and day-ahead electricity prices. This article is part of the theme issue ‘The mathematics of energy systems’.

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