IDEAS home Printed from https://ideas.repec.org/a/spr/sistpr/v25y2022i3d10.1007_s11203-021-09263-3.html
   My bibliography  Save this article

Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces

Author

Listed:
  • Michel Harel

    (Institut de Mathématiques de Toulouse
    Université de Limoges)

  • Joseph Ngatchou-Wandji

    (EHESP Rennes & Institut Élie Cartan de Lorraine)

  • Livasoa Andriamampionona

    (University of Antananarivo)

  • Victor Harison

    (University of Antananarivo)

Abstract

This paper deals with the weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces. It is an extension of Harel et al. (J Math Anal Appl 189:240–255, 1995) from the one-dimensional case to the multivariate and multidimensional case. The estimators are based on a sequence of non-negative independent and identically distributed (iid) random vectors. They are expressed as infinite sums of k-folds convolutions of the empirical distribution function. Their weak convergence study heavily rests on that of the empirical distribution function.

Suggested Citation

  • Michel Harel & Joseph Ngatchou-Wandji & Livasoa Andriamampionona & Victor Harison, 2022. "Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 485-504, October.
    • Handle: RePEc:spr:sistpr:v:25:y:2022:i:3:d:10.1007_s11203-021-09263-3
    DOI: 10.1007/s11203-021-09263-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11203-021-09263-3
    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/s11203-021-09263-3?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. Edward W. Frees, 1986. "Warranty analysis and renewal function estimation," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(3), pages 361-372, August.
    2. P. C. B. Phillips & S. N. Durlauf, 1986. "Multiple Time Series Regression with Integrated Processes," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 53(4), pages 473-495.
    3. Frees, Edward W, 1988. "Estimating the Cost of a Warranty," Journal of Business & Economic Statistics, American Statistical Association, vol. 6(1), pages 79-86, January.
    4. Wooldridge, Jeffrey M. & White, Halbert, 1988. "Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 4(2), pages 210-230, August.
    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. Cheol-Keun Cho & Timothy J. Vogelsang, 2016. "Fixed- b Inference for Testing Structural Change in a Time Series Regression," Econometrics, MDPI, vol. 5(1), pages 1-26, December.
    2. Yikang, Li, 1998. "Low-pass filtered least squares estimators of cointegrating vectors," Journal of Econometrics, Elsevier, vol. 85(2), pages 289-316, August.
    3. Christis Katsouris, 2022. "Partial Sum Processes of Residual-Based and Wald-type Break-Point Statistics in Time Series Regression Models," Papers 2202.00141, arXiv.org, revised Feb 2022.
    4. Cosme Vodounou, 1998. "Inférence fondée sur les statistiques des rendements de long terme," CIRANO Working Papers 98s-20, CIRANO.
    5. Christis Katsouris, 2023. "Limit Theory under Network Dependence and Nonstationarity," Papers 2308.01418, arXiv.org, revised Aug 2023.
    6. Guili Liao & Qimeng Liu & Rongmao Zhang & Shifang Zhang, 2022. "Rank test of unit‐root hypothesis with AR‐GARCH errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(5), pages 695-719, September.
    7. Arai, Yoichi, 2016. "Testing For Linearity In Regressions With I(1) Processes," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 57(1), pages 111-138, June.
    8. Liu, Bingqi & Pang, Tianxiao & Cheng, Siang, 2024. "Estimation for generalized linear cointegration regression models through composite quantile regression approach," Finance Research Letters, Elsevier, vol. 65(C).
    9. Matteo Mogliani, 2010. "Residual-based tests for cointegration and multiple deterministic structural breaks: A Monte Carlo study," Working Papers halshs-00564897, HAL.
    10. Postel-Vinay, Fabien & Jolivet, Grégory & Borowczyk-Martins, Daniel, 2011. "Accounting For Endogenous Search Behavior in Matching Function Estimation," CEPR Discussion Papers 8471, C.E.P.R. Discussion Papers.
    11. Choi, In & Kurozumi, Eiji, 2012. "Model selection criteria for the leads-and-lags cointegrating regression," Journal of Econometrics, Elsevier, vol. 169(2), pages 224-238.
    12. Palm, Franz C. & Smeekes, Stephan & Urbain, Jean-Pierre, 2011. "Cross-sectional dependence robust block bootstrap panel unit root tests," Journal of Econometrics, Elsevier, vol. 163(1), pages 85-104, July.
    13. Koo, Bonsoo & Seo, Myung Hwan, 2015. "Structural-break models under mis-specification: Implications for forecasting," Journal of Econometrics, Elsevier, vol. 188(1), pages 166-181.
    14. Muhammad Shahbaz & Pervaz Azim & Khalil Ahmad, 2011. "Exports-Led Growth Hypothesis in Pakistan: Further Evidence," Asian Economic and Financial Review, Asian Economic and Social Society, vol. 1(3), pages 182-197.
    15. repec:hum:wpaper:sfb649dp2007-042 is not listed on IDEAS
    16. Sokbae Lee & Myung Hwan Seo & Youngki Shin, 2017. "Correction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 883-883, April.
    17. Fiteni, Inmaculada, 2004. "[tau]-estimators of regression models with structural change of unknown location," Journal of Econometrics, Elsevier, vol. 119(1), pages 19-44, March.
    18. Lee, Jungyoon & Robinson, Peter M., 2016. "Series estimation under cross-sectional dependence," Journal of Econometrics, Elsevier, vol. 190(1), pages 1-17.
    19. Herwartz, Helmut & Neumann, Michael H., 2005. "Bootstrap inference in systems of single equation error correction models," Journal of Econometrics, Elsevier, vol. 128(1), pages 165-193, September.
    20. Ventosa-Santaulària Daniel & Gómez-Zaldívar Manuel, 2011. "Testing for a Deterministic Trend When There is Evidence of Unit Root," Journal of Time Series Econometrics, De Gruyter, vol. 2(2), pages 1-26, January.
    21. Jungbin Hwang & Gonzalo Valdés, 2020. "Low Frequency Cointegrating Regression in the Presence of Local to Unity Regressors and Unknown Form of Serial Dependence," Working papers 2020-03, University of Connecticut, Department of Economics, revised Aug 2020.

    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:sistpr:v:25:y:2022:i:3:d:10.1007_s11203-021-09263-3. 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.