IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v35y2022i2d10.1007_s10959-021-01075-8.html
   My bibliography  Save this article

Distances Between Distributions Via Stein’s Method

Author

Listed:
  • Marie Ernst

    (Université de Liège)

  • Yvik Swan

    (Université libre de Bruxelles)

Abstract

We build on the formalism developed in Ernst et al. (First order covariance inequalities via Stein’s method, 2019) to propose new representations of solutions to Stein equations. We provide new uniform and nonuniform bounds on these solutions (a.k.a. Stein factors). We use these representations to obtain representations for differences between expectations in terms of solutions to the Stein equations. We apply these to compute abstract Stein-type bounds on Kolmogorov, total variation and Wasserstein distances between arbitrary distributions. We apply our results to several illustrative examples and compare our results with current literature on the same topic, whenever possible. In all occurrences our results are competitive.

Suggested Citation

  • Marie Ernst & Yvik Swan, 2022. "Distances Between Distributions Via Stein’s Method," Journal of Theoretical Probability, Springer, vol. 35(2), pages 949-987, June.
    • Handle: RePEc:spr:jotpro:v:35:y:2022:i:2:d:10.1007_s10959-021-01075-8
    DOI: 10.1007/s10959-021-01075-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-021-01075-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10959-021-01075-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Alison L. Gibbs & Francis Edward Su, 2002. "On Choosing and Bounding Probability Metrics," International Statistical Review, International Statistical Institute, vol. 70(3), pages 419-435, December.
    2. Ehm, Werner, 1991. "Binomial approximation to the Poisson binomial distribution," Statistics & Probability Letters, Elsevier, vol. 11(1), pages 7-16, January.
    3. Larry Goldstein & Gesine Reinert, 2005. "Distributional Transformations, Orthogonal Polynomials, and Stein Characterizations," Journal of Theoretical Probability, Springer, vol. 18(1), pages 237-260, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. 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.
    3. Arun G. Chandrasekhar & Robert Townsend & Juan Pablo Xandri, 2018. "Financial Centrality and Liquidity Provision," NBER Working Papers 24406, National Bureau of Economic Research, Inc.
    4. Gerhold, Stefan & Gülüm, I. Cetin, 2019. "Peacocks nearby: Approximating sequences of measures," Stochastic Processes and their Applications, Elsevier, vol. 129(7), pages 2406-2436.
    5. David M. Phillippo & Sofia Dias & A. E. Ades & Mark Belger & Alan Brnabic & Alexander Schacht & Daniel Saure & Zbigniew Kadziola & Nicky J. Welton, 2020. "Multilevel network meta‐regression for population‐adjusted treatment comparisons," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 183(3), pages 1189-1210, June.
    6. Xuejun Zhao & Ruihao Zhu & William B. Haskell, 2022. "Learning to Price Supply Chain Contracts against a Learning Retailer," Papers 2211.04586, arXiv.org.
    7. 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.
    8. 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).
    9. 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.
    10. 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.
    11. 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.
    12. Róbert Pethes & Levente Kovács, 2023. "An Exact and an Approximation Method to Compute the Degree Distribution of Inhomogeneous Random Graph Using Poisson Binomial Distribution," Mathematics, MDPI, vol. 11(6), pages 1-24, March.
    13. 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.
    14. Leandro Nascimento, 2022. "Bounded arbitrage and nearly rational behavior," Papers 2212.02680, arXiv.org, revised Jul 2023.
    15. 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.
    16. 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.
    17. Patrick Marsh, 2019. "The role of information in nonstationary regression," Discussion Papers 19/04, University of Nottingham, Granger Centre for Time Series Econometrics.
    18. 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.
    19. 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.
    20. 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.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jotpro:v:35:y:2022:i:2:d:10.1007_s10959-021-01075-8. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.