IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v212y2024ics0167715224001263.html

Nonparametric inference for NBUE distributions based on the TTT transform

Author

Listed:
  • Lando, Tommaso

Abstract

This paper presents a uniformly consistent estimator for the cumulative distribution function, operating under the assumption of “new better than used in expectation” (NBUE). Additionally, it introduces a novel class of consistent tests for the NBUE null hypothesis. Both procedures leverage the empirical total time on test (TTT) transform. Finite sample properties of the proposed methods are investigated through simulations.

Suggested Citation

  • Lando, Tommaso, 2024. "Nonparametric inference for NBUE distributions based on the TTT transform," Statistics & Probability Letters, Elsevier, vol. 212(C).
    • Handle: RePEc:eee:stapro:v:212:y:2024:i:c:s0167715224001263
    DOI: 10.1016/j.spl.2024.110157
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224001263
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110157?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Mark Brown, 2013. "Sharp bounds for NBUE distributions," Annals of Operations Research, Springer, vol. 208(1), pages 245-250, September.
    2. Lando, Tommaso, 2023. "Testing departures from the increasing hazard rate property," Statistics & Probability Letters, Elsevier, vol. 193(C).
    3. Kan Cheng & Yeh Lam, 2002. "Reliability bounds for the NBUE distributions," Naval Research Logistics (NRL), John Wiley & Sons, vol. 49(8), pages 781-797, December.
    4. Rojo, J. & Samaniego, F. J., 1994. "Uniform Strong Consistent Estimation of an Ifra Distribution Function," Journal of Multivariate Analysis, Elsevier, vol. 49(1), pages 150-163, April.
    5. Richard E. Barlow, 1979. "Geometry of the total time on test transform," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 26(3), pages 393-402, September.
    6. Anis, M.Z. & Mitra, M., 2011. "A generalized Hollander-Proschan type test for NBUE alternatives," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 126-132, January.
    7. Zheng Fang & Andres Santos, 2019. "Inference on Directionally Differentiable Functions," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 86(1), pages 377-412.
    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. Ruhul Ali Khan & Dhrubasish Bhattacharyya & Murari Mitra, 2021. "Exact and asymptotic tests of exponentiality against nonmonotonic mean time to failure type alternatives," Statistical Papers, Springer, vol. 62(6), pages 3015-3045, December.
    2. Mika Meitz, 2024. "Statistical inference for generative adversarial networks and other minimax problems," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1323-1356, September.
    3. Firpo, Sergio & Galvao, Antonio F. & Kobus, Martyna & Parker, Thomas & Rosa-Dias, Pedro, 2025. "Loss aversion and the welfare ranking of policy interventions," Journal of Econometrics, Elsevier, vol. 252(PB).
    4. Hyunju Son & Youyi Fong, 2021. "Fast grid search and bootstrap‐based inference for continuous two‐phase polynomial regression models," Environmetrics, John Wiley & Sons, Ltd., vol. 32(3), May.
    5. Lee, Kyungho & Linton, Oliver & Whang, Yoon-Jae, 2023. "Testing for time stochastic dominance," Journal of Econometrics, Elsevier, vol. 235(2), pages 352-371.
    6. Kai Feng & Han Hong & Denis Nekipelov, 2024. "Statistical Inference of Optimal Allocations I: Regularities and their Implications," Papers 2403.18248, arXiv.org, revised Feb 2026.
    7. Sungwon Lee, 2024. "Partial identification and inference for conditional distributions of treatment effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 107-127, January.
    8. Hundrieser, Shayan & Mordant, Gilles & Weitkamp, Christoph A. & Munk, Axel, 2024. "Empirical optimal transport under estimated costs: Distributional limits and statistical applications," Stochastic Processes and their Applications, Elsevier, vol. 178(C).
    9. Firpo, Sergio & Galvao, Antonio F. & Parker, Thomas, 2023. "Uniform inference for value functions," Journal of Econometrics, Elsevier, vol. 235(2), pages 1680-1699.
    10. Kitagawa, Toru & Montiel Olea, José Luis & Payne, Jonathan & Velez, Amilcar, 2020. "Posterior distribution of nondifferentiable functions," Journal of Econometrics, Elsevier, vol. 217(1), pages 161-175.
    11. Bastian, P. & Dette, H. & Koletzko, L., 2024. "Testing equivalence of multinomial distributions — A constrained bootstrap approach," Statistics & Probability Letters, Elsevier, vol. 206(C).
    12. Zhexiao Lin & Fang Han, 2023. "On the failure of the bootstrap for Chatterjee's rank correlation," Papers 2303.14088, arXiv.org, revised Apr 2023.
    13. Xiaojun Song & Zhenting Sun, 2023. "Almost Dominance: Inference and Application," Papers 2312.02288, arXiv.org, revised Oct 2025.
    14. Wang, Dewei & Tang, Chuan-Fa & Tebbs, Joshua M., 2020. "More powerful goodness-of-fit tests for uniform stochastic ordering," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    15. Mogstad, Magne & Torgovitsky, Alexander, 2024. "Instrumental variables with unobserved heterogeneity in treatment effects," Handbook of Labor Economics,, Elsevier.
    16. Callaway, Brantly, 2021. "Bounds on distributional treatment effect parameters using panel data with an application on job displacement," Journal of Econometrics, Elsevier, vol. 222(2), pages 861-881.
    17. Keisuke Hirano & Jack R. Porter, 2023. "Asymptotic Representations for Sequential Decisions, Adaptive Experiments, and Batched Bandits," Papers 2302.03117, arXiv.org, revised Feb 2025.
    18. Romuald Meango & Marc Henry & Ismael Mourifie, 2025. "Combining stated and revealed preferences," Papers 2507.13552, arXiv.org, revised Nov 2025.
    19. Xinyue Bei & Manu Navjeevan, 2026. "Inference under First-Order Degeneracy," Papers 2602.07377, arXiv.org.
    20. Ghosh, Shyamal & Mitra, Murari, 2017. "A weighted integral approach to testing against HNBUE alternatives," Statistics & Probability Letters, Elsevier, vol. 129(C), pages 58-64.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    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:eee:stapro:v:212:y:2024:i:c:s0167715224001263. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.