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On Choosing and Bounding Probability Metrics

Citations

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Cited by:

  1. Antonio Irpino & Rosanna Verde, 2015. "Basic statistics for distributional symbolic variables: a new metric-based approach," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(2), pages 143-175, June.
  2. Marie Ernst & Yvik Swan, 2022. "Distances Between Distributions Via Stein’s Method," Journal of Theoretical Probability, Springer, vol. 35(2), pages 949-987, June.
  3. Wei Wang & Huifu Xu & Tiejun Ma, 2020. "Quantitative Statistical Robustness for Tail-Dependent Law Invariant Risk Measures," Papers 2006.15491, arXiv.org.
  4. Rosaria Simone, 2022. "On finite mixtures of Discretized Beta model for ordered responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(3), pages 828-855, September.
  5. Arno Berger & Chuang Xu, 2020. "Asymptotics of One-Dimensional Lévy Approximations," Journal of Theoretical Probability, Springer, vol. 33(2), pages 1164-1195, June.
  6. Yining Gu & Yanjun Wang & Zhen Cao & Yicheng Huang, 2026. "Distributionally robust optimization problem with probabilistic envelope constraints over Wasserstein ball," Computational Optimization and Applications, Springer, vol. 93(3), pages 1145-1189, April.
  7. Berrendero, José R. & Cuevas, Antonio & Pateiro-López, Beatriz, 2016. "Shape classification based on interpoint distance distributions," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 237-247.
  8. Zellinger, Werner & Moser, Bernhard A., 2021. "On the truncated Hausdorff moment problem under Sobolev regularity conditions," Applied Mathematics and Computation, Elsevier, vol. 400(C).
  9. Harrison Katz, 2025. "Impact by design: translating Lead times in flux into an R handbook with code," Papers 2511.12763, arXiv.org, revised Nov 2025.
  10. Jitka Hrabáková & Václav Kůs, 2017. "Notes on consistency of some minimum distance estimators with simulation results," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(2), pages 243-257, February.
  11. Giacomo Aletti & Caterina May & Piercesare Secchi, 2012. "A Functional Equation Whose Unknown is $\mathcal{P}([0,1])$ Valued," Journal of Theoretical Probability, Springer, vol. 25(4), pages 1207-1232, December.
  12. Li, Manlan & Xu, Huifu, 2025. "A modified late arrival penalized user equilibrium model and robustness in data perturbation," Transportation Research Part B: Methodological, Elsevier, vol. 199(C).
  13. Daniel Commenges & Anne Gégout‐Petit, 2009. "A general dynamical statistical model with causal interpretation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 719-736, June.
  14. Fabian Krüger & Sebastian Lerch & Thordis Thorarinsdottir & Tilmann Gneiting, 2021. "Predictive Inference Based on Markov Chain Monte Carlo Output," International Statistical Review, International Statistical Institute, vol. 89(2), pages 274-301, August.
  15. Alberto Muñoz & Gabriel Martos & Javier Gonzalez, 2023. "Level Sets Semimetrics for Probability Measures with Applications in Hypothesis Testing," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-17, March.
  16. Gurdip Bakshi & Xiaohui Gao & George Panayotov, 2021. "A Theory of Dissimilarity Between Stochastic Discount Factors," Management Science, INFORMS, vol. 67(7), pages 4602-4622, July.
  17. Arno Berger & Theodore P. Hill & Kent E. Morrison, 2008. "Scale-Distortion Inequalities for Mantissas of Finite Data Sets," Journal of Theoretical Probability, Springer, vol. 21(1), pages 97-117, March.
  18. Crimaldi, Irene & Dai Pra, Paolo & Louis, Pierre-Yves & Minelli, Ida G., 2019. "Synchronization and functional central limit theorems for interacting reinforced random walks," Stochastic Processes and their Applications, Elsevier, vol. 129(1), pages 70-101.
  19. Hafouta, Yeor & Kifer, Yuri, 2016. "Berry–Esseen type estimates for nonconventional sums," Stochastic Processes and their Applications, Elsevier, vol. 126(8), pages 2430-2464.
  20. Cheng, Lingyan & Wu, Liming, 2019. "Centered Sobolev inequality and exponential convergence in Φ-entropy," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 101-111.
  21. Katriel, Guy, 2019. "A quantitative discounted central limit theorem using the Fourier metric," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 321-326.
  22. Patrick Marsh, "undated". "A Measure of Distance for the Unit Root Hypothesis," Discussion Papers 05/02, Department of Economics, University of York.
  23. Corrado Crocetta & Antonio Irpino & Laura Antonucci & Claudia Marin, 2025. "A performance indicator and its decomposition according to the impacts of different aspects based on distributional data," Quality & Quantity: International Journal of Methodology, Springer, vol. 59(3), pages 2091-2110, June.
  24. Joseph D. Bailey & Edward A. Codling, 2021. "Emergence of the wrapped Cauchy distribution in mixed directional data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 105(2), pages 229-246, June.
  25. Barrera, Javiera & Lachaud, Béatrice & Ycart, Bernard, 2006. "Cut-off for n-tuples of exponentially converging processes," Stochastic Processes and their Applications, Elsevier, vol. 116(10), pages 1433-1446, October.
  26. Puppo, L. & Pedroni, N. & Maio, F. Di & Bersano, A. & Bertani, C. & Zio, E., 2021. "A Framework based on Finite Mixture Models and Adaptive Kriging for Characterizing Non-Smooth and Multimodal Failure Regions in a Nuclear Passive Safety System," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
  27. White, Staci A. & Herbei, Radu, 2015. "A Monte Carlo approach to quantifying model error in Bayesian parameter estimation," Computational Statistics & Data Analysis, Elsevier, vol. 83(C), pages 168-181.
  28. Oyama, Daisuke & Tercieux, Olivier, 2012. "On the strategic impact of an event under non-common priors," Games and Economic Behavior, Elsevier, vol. 74(1), pages 321-331.
  29. El Mehdi Haress & Alexandre Richard, 2024. "Estimation of several parameters in discretely-observed stochastic differential equations with additive fractional noise," Statistical Inference for Stochastic Processes, Springer, vol. 27(3), pages 641-691, October.
  30. Ira W. Herbst & Jesper Møller & Anne Marie Svane, 2024. "How Many Digits are Needed?," Methodology and Computing in Applied Probability, Springer, vol. 26(1), pages 1-13, March.
  31. Sebastian Sitarz, 2013. "Compromise programming with Tchebycheff norm for discrete stochastic orders," Annals of Operations Research, Springer, vol. 211(1), pages 433-446, December.
  32. Xuejun Zhao & Ruihao Zhu & William B. Haskell, 2022. "Learning to Price Supply Chain Contracts against a Learning Retailer," Papers 2211.04586, arXiv.org.
  33. Arroyo, Javier & Maté, Carlos, 2009. "Forecasting histogram time series with k-nearest neighbours methods," International Journal of Forecasting, Elsevier, vol. 25(1), pages 192-207.
  34. Sainan Zhang & Huifu Xu, 2022. "Insurance premium-based shortfall risk measure induced by cumulative prospect theory," Computational Management Science, Springer, vol. 19(4), pages 703-738, October.
  35. Kavita Ramanan & Aaron Smith, 2018. "Bounds on Lifting Continuous-State Markov Chains to Speed Up Mixing," Journal of Theoretical Probability, Springer, vol. 31(3), pages 1647-1678, September.
  36. Frédéric Ouimet, 2024. "Deficiency bounds for the multivariate inverse hypergeometric distribution," Statistical Papers, Springer, vol. 65(6), pages 3959-3969, August.
  37. Lahkar, Ratul & Riedel, Frank, 2016. "The Continuous Logit Dynamic and Price Dispersion," Center for Mathematical Economics Working Papers 521, Center for Mathematical Economics, Bielefeld University.
  38. Hong T. M. Chu & Meixia Lin & Kim-Chuan Toh, 2026. "Wasserstein Distributionally Robust Optimization and Its Tractable Regularization Formulation," Journal of Optimization Theory and Applications, Springer, vol. 208(2), pages 1-28, February.
  39. Francisco de A. T. Carvalho & Antonio Irpino & Rosanna Verde & Antonio Balzanella, 2022. "Batch Self-Organizing Maps for Distributional Data with an Automatic Weighting of Variables and Components," Journal of Classification, Springer;The Classification Society, vol. 39(2), pages 343-375, July.
  40. Ana C. Gómez Ugarte Valerio & Ugofilippo Basellini & Carlo G. Camarda & Fanny Janssen & Emilio Zagheni, 2024. "Reassessing socioeconomic inequalities in mortality via distributional similarities," MPIDR Working Papers WP-2024-007, Max Planck Institute for Demographic Research, Rostock, Germany.
  41. Beh, Eric J. & Lombardo, Rosaria & Alberti, Gianmarco, 2018. "Correspondence analysis and the Freeman–Tukey statistic: A study of archaeological data," Computational Statistics & Data Analysis, Elsevier, vol. 128(C), pages 73-86.
  42. Leandro Nascimento, 2024. "Bounded arbitrage and nearly rational behavior," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 77(4), pages 941-974, June.
  43. Postek, K.S. & den Hertog, D. & Melenberg, B., 2015. "Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures (revision of CentER DP 2014-031)," Other publications TiSEM eeb9c898-6943-4199-b747-3, Tilburg University, School of Economics and Management.
  44. Yannan Chen & Hailin Sun & Huifu Xu, 2021. "Decomposition and discrete approximation methods for solving two-stage distributionally robust optimization problems," Computational Optimization and Applications, Springer, vol. 78(1), pages 205-238, January.
  45. Crimaldi, Irene & Dai Pra, Paolo & Minelli, Ida Germana, 2016. "Fluctuation theorems for synchronization of interacting Pólya’s urns," Stochastic Processes and their Applications, Elsevier, vol. 126(3), pages 930-947.
  46. HAEDO , Christian & Mouchart, Michel, 2011. "A Stochastic Independence Approach for different Measures of Global Specialization," LIDAM Discussion Papers ISBA 2011006, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
  47. Lijun Cheng & Pratik Karkhanis & Birkan Gokbag & Yueze Liu & Lang Li, 2022. "DGCyTOF: Deep learning with graphic cluster visualization to predict cell types of single cell mass cytometry data," PLOS Computational Biology, Public Library of Science, vol. 18(4), pages 1-22, April.
  48. Di Maio, Francesco & Bandini, Alessandro & Zio, Enrico & Alberola, Sofia Carlos & Sanchez-Saez, Francisco & Martorell, Sebastián, 2016. "Bootstrapped-ensemble-based Sensitivity Analysis of a trace thermal-hydraulic model based on a limited number of PWR large break loca simulations," Reliability Engineering and System Safety, Elsevier, vol. 153(C), pages 122-134.
  49. Marcel Favereau & Frédéric Babonneau & Álvaro Lorca, 2026. "Water resources management: a bibliometric analysis and future research directions," Annals of Operations Research, Springer, vol. 358(2), pages 533-588, March.
  50. A. Burak Paç & Mustafa Ç. Pınar, 2018. "On robust portfolio and naïve diversification: mixing ambiguous and unambiguous assets," Annals of Operations Research, Springer, vol. 266(1), pages 223-253, July.
  51. Fontem, Belleh & Ji, Ran, 2026. "Distributionally robust optimization with generalized total variation ambiguity sets," European Journal of Operational Research, Elsevier, vol. 328(3), pages 894-911.
  52. Yongchao Liu & Alois Pichler & Huifu Xu, 2019. "Discrete Approximation and Quantification in Distributionally Robust Optimization," Mathematics of Operations Research, INFORMS, vol. 44(1), pages 19-37, February.
  53. Tomas Folke & Giulia Bertoldo & Darlene D’Souza & Sonia Alì & Federica Stablum & Kai Ruggeri, 2021. "Boosting promotes advantageous risk-taking," Humanities and Social Sciences Communications, Palgrave Macmillan, vol. 8(1), pages 1-10, December.
  54. Postek, K.S. & den Hertog, D. & Melenberg, B., 2015. "Computationally Tractable Counterparts of Distributionally Robust Constraints on Risk Measures (revision of CentER DP 2014-031)," Discussion Paper 2015-047, Tilburg University, Center for Economic Research.
  55. Bertanha, Marinho & Moreira, Marcelo J., 2020. "Impossible inference in econometrics: Theory and applications," Journal of Econometrics, Elsevier, vol. 218(2), pages 247-270.
  56. Pesenti, Silvana M. & Millossovich, Pietro & Tsanakas, Andreas, 2019. "Reverse sensitivity testing: What does it take to break the model?," European Journal of Operational Research, Elsevier, vol. 274(2), pages 654-670.
  57. Max Grieshammer & Lukas Pflug & Michael Stingl & Andrian Uihlein, 2024. "The continuous stochastic gradient method: part I–convergence theory," Computational Optimization and Applications, Springer, vol. 87(3), pages 935-976, April.
  58. Arno Berger & Chuang Xu, 2019. "Best Finite Approximations of Benford’s Law," Journal of Theoretical Probability, Springer, vol. 32(3), pages 1525-1553, September.
  59. Teferra, Kirubel & Shields, Michael D. & Hapij, Adam & Daddazio, Raymond P., 2014. "Mapping model validation metrics to subject matter expert scores for model adequacy assessment," Reliability Engineering and System Safety, Elsevier, vol. 132(C), pages 9-19.
  60. David Wozabal, 2012. "A framework for optimization under ambiguity," Annals of Operations Research, Springer, vol. 193(1), pages 21-47, March.
  61. Moritz Nobis & Carlo Schmitt & Ralf Schemm & Armin Schnettler, 2020. "Pan-European CVaR-Constrained Stochastic Unit Commitment in Day-Ahead and Intraday Electricity Markets," Energies, MDPI, vol. 13(9), pages 1-35, May.
  62. Schneider, Judith C. & Schweizer, Nikolaus, 2015. "Robust measurement of (heavy-tailed) risks: Theory and implementation," Journal of Economic Dynamics and Control, Elsevier, vol. 61(C), pages 183-203.
  63. Fabian R. Pieroth & Tuomas Sandholm, 2024. "Verifying Approximate Equilibrium in Auctions," Papers 2408.11445, arXiv.org.
  64. HAEDO, Christian & MOUCHART, Michel, 2012. "A stochastic independence approach for different measures of concentration and specialization," LIDAM Discussion Papers CORE 2012025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  65. Laura Azzimonti & Francesca Ieva & Anna Maria Paganoni, 2013. "Nonlinear nonparametric mixed-effects models for unsupervised classification," Computational Statistics, Springer, vol. 28(4), pages 1549-1570, August.
  66. Hoang, Lê Nguyên & Soumis, François & Zaccour, Georges, 2019. "The return function: A new computable perspective on Bayesian–Nash equilibria," European Journal of Operational Research, Elsevier, vol. 279(2), pages 471-485.
  67. Ouimet, Frédéric, 2022. "A symmetric matrix-variate normal local approximation for the Wishart distribution and some applications," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
  68. Takashi Kamihigashi & John Stachurski, 2017. "Some Unified Results for Classical and Monotone Markov Chain Theory," Discussion Paper Series DP2017-02, Research Institute for Economics & Business Administration, Kobe University.
  69. Pflug, Georg Ch. & Pichler, Alois & Wozabal, David, 2012. "The 1/N investment strategy is optimal under high model ambiguity," Journal of Banking & Finance, Elsevier, vol. 36(2), pages 410-417.
  70. Stephan Eckstein & Gaoyue Guo & Tongseok Lim & Jan Obloj, 2019. "Robust pricing and hedging of options on multiple assets and its numerics," Papers 1909.03870, arXiv.org, revised Oct 2020.
  71. Gerhold, Stefan & Gülüm, I. Cetin, 2019. "Peacocks nearby: Approximating sequences of measures," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2406-2436.
  72. Matheus Henrique Junqueira Saldanha & Adriano Kamimura Suzuki, 2023. "On dealing with the unknown population minimum in parametric inference," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 509-535, September.
  73. Kim, Junhyong & Mossel, Elchanan & Rácz, Miklós Z. & Ross, Nathan, 2015. "Can one hear the shape of a population history?," Theoretical Population Biology, Elsevier, vol. 100(C), pages 26-38.
  74. Sergiu Hart & Noam Nisan, 2025. "The Root of Revenue Continuity," Papers 2507.15735, arXiv.org, revised Jan 2026.
  75. Alexander Bulinski & Nikolay Slepov, 2022. "Sharp Estimates for Proximity of Geometric and Related Sums Distributions to Limit Laws," Mathematics, MDPI, vol. 10(24), pages 1-37, December.
  76. Wang, Wei & Maio, Francesco Di & Zio, Enrico, 2017. "Three-loop Monte Carlo simulation approach to Multi-State Physics Modeling for system reliability assessment," Reliability Engineering and System Safety, Elsevier, vol. 167(C), pages 276-289.
  77. Daniela Hurtado-Lange & Siva Theja Maguluri, 2022. "A load balancing system in the many-server heavy-traffic asymptotics," Queueing Systems: Theory and Applications, Springer, vol. 101(3), pages 353-391, August.
  78. Leskelä, Lasse & Vihola, Matti, 2013. "Stochastic order characterization of uniform integrability and tightness," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 382-389.
  79. Jiekun Feng & Pengyi Shi, 2018. "Steady‐state diffusion approximations for discrete‐time queue in hospital inpatient flow management," Naval Research Logistics (NRL), John Wiley & Sons, vol. 65(1), pages 26-65, February.
  80. Christophe Ley & Gesine Reinert & Yvik Swan, 2014. "Approximate Computation of Expectations: the Canonical Stein Operator," Working Papers ECARES ECARES 2014-36, ULB -- Universite Libre de Bruxelles.
  81. Plischke, Elmar & Borgonovo, Emanuele & Smith, Curtis L., 2013. "Global sensitivity measures from given data," European Journal of Operational Research, Elsevier, vol. 226(3), pages 536-550.
  82. Fenner, Trevor & Levene, Mark & Loizou, George, 2010. "Predicting the long tail of book sales: Unearthing the power-law exponent," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2416-2421.
  83. Wu, Qiong & Wang, Wei & Zhang, Sainan & Xu, Huifu, 2025. "Bi-attribute utility preference robust optimization: A continuous piecewise linear approximation approach," European Journal of Operational Research, Elsevier, vol. 323(1), pages 170-191.
  84. Martos, Gabriel, 2013. "A new distance for data sets (and probability measures) in a RKHS context," DES - Working Papers. Statistics and Econometrics. WS ws131514, Universidad Carlos III de Madrid. Departamento de Estadística.
  85. Peng Liu & Alexander Schied, 2025. "Lambda Value-at-Risk under ambiguity and risk sharing," Papers 2511.00717, arXiv.org.
  86. Abhijnan Rej, 2013. "Modeling systemic risks in financial markets," Papers 1311.3764, arXiv.org.
  87. Borgonovo, E. & Zentner, I. & Pellegri, A. & Tarantola, S. & de Rocquigny, E., 2013. "On the importance of uncertain factors in seismic fragility assessment," Reliability Engineering and System Safety, Elsevier, vol. 109(C), pages 66-76.
  88. Francesco Di Maio & Nicola Pedroni & Barnabás Tóth & Luciano Burgazzi & Enrico Zio, 2021. "Reliability Assessment of Passive Safety Systems for Nuclear Energy Applications: State-of-the-Art and Open Issues," Energies, MDPI, vol. 14(15), pages 1-17, August.
  89. Patrick Marsh, 2019. "The role of information in nonstationary regression," Discussion Papers 19/04, University of Nottingham, Granger Centre for Time Series Econometrics.
  90. Leandro Nascimento, 2022. "Bounded arbitrage and nearly rational behavior," Papers 2212.02680, arXiv.org, revised Apr 2025.
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