IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v56y2015i3p887-910.html
   My bibliography  Save this article

A kernel mode estimate under random left truncation and time series model: asymptotic normality

Author

Listed:
  • Ouafae Benrabah
  • Elias Ould Saïd
  • Abdelkader Tatachak

Abstract

Let $$\left\{ Y_{N}, N\ge 1\right\} $$ Y N , N ≥ 1 be a sequence of random variables of interest and $$\left\{ T_{N}, N\ge 1\right\} $$ T N , N ≥ 1 be a sequence of truncating variables. For a given $$n-$$ n - sample $$\left( n\le N\right) $$ n ≤ N of truncated replicates of $$Y$$ Y fulfilling the $$\alpha -$$ α - mixing condition, we establish asymptotic normality and construct confidence intervals for a proposed kernel mode estimator (say, $$\widehat{\theta }_n$$ θ ^ n ) of the true mode $$\theta $$ θ of $$Y$$ Y . Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Ouafae Benrabah & Elias Ould Saïd & Abdelkader Tatachak, 2015. "A kernel mode estimate under random left truncation and time series model: asymptotic normality," Statistical Papers, Springer, vol. 56(3), pages 887-910, August.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:3:p:887-910
    DOI: 10.1007/s00362-014-0613-7
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-014-0613-7
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-014-0613-7?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. Herrmann, Eva & Ziegler, Klaus, 2004. "Rates of consistency for nonparametric estimation of the mode in absence of smoothness assumptions," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 359-368, July.
    2. Quintela-del-Rio, Alejandro, 2007. "Plug-in bandwidth selection in kernel hazard estimation from dependent data," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5800-5812, August.
    3. Dominik Wied & Rafael Weißbach, 2012. "Consistency of the kernel density estimator: a survey," Statistical Papers, Springer, vol. 53(1), pages 1-21, February.
    4. Vieu, Philippe, 1996. "A note on density mode estimation," Statistics & Probability Letters, Elsevier, vol. 26(4), pages 297-307, March.
    5. Cai, Zongwu, 1998. "Asymptotic properties of Kaplan-Meier estimator for censored dependent data," Statistics & Probability Letters, Elsevier, vol. 37(4), pages 381-389, March.
    6. Li, Yun-Xia & Wang, Jian-Feng, 2008. "An almost sure central limit theorem for products of sums under association," Statistics & Probability Letters, Elsevier, vol. 78(4), pages 367-375, March.
    7. Scott, David W., 2004. "Multivariate Density Estimation and Visualization," Papers 2004,16, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    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. Eunju Hwang & Dong Shin, 2016. "Kernel estimators of mode under $$\psi $$ ψ -weak dependence," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 68(2), pages 301-327, April.
    2. Salah Khardani & Mohamed Lemdani & Elias Ould Saïd, 2012. "On the strong uniform consistency of the mode estimator for censored time series," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 229-241, February.
    3. Obereder, Andreas & Scherzer, Otmar & Kovac, Arne, 2007. "Bivariate density estimation using BV regularisation," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 5622-5634, August.
    4. Shi, Xiaoping & Wu, Yuehua & Miao, Baiqi, 2009. "A note on the convergence rate of the kernel density estimator of the mode," Statistics & Probability Letters, Elsevier, vol. 79(17), pages 1866-1871, September.
    5. Han-Ying Liang & Jacobo Uña-Álvarez, 2010. "Asymptotic normality for estimator of conditional mode under left-truncated and dependent observations," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(1), pages 1-19, July.
    6. Tang, Linjun & Zhou, Zhangong & Wu, Changchun, 2012. "Weighted composite quantile estimation and variable selection method for censored regression model," Statistics & Probability Letters, Elsevier, vol. 82(3), pages 653-663.
    7. Jingle Wang & Ming Zheng, 2012. "Wavelet detection of change points in hazard rate models with censored dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(3), pages 765-781.
    8. Giovanni Paolo Crespi & Elisa Mastrogiacomo, 2020. "Qualitative robustness of set-valued value-at-risk," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 91(1), pages 25-54, February.
    9. R. Zamini & V. Fakoor & M. Sarmad, 2015. "On estimation of a density function in multiplicative censoring," Statistical Papers, Springer, vol. 56(3), pages 661-676, August.
    10. Sun, Liuquan & Zhou, Xian, 2001. "Survival function and density estimation for truncated dependent data," Statistics & Probability Letters, Elsevier, vol. 52(1), pages 47-57, March.
    11. Yi Wu & Wei Yu & Xuejun Wang, 2022. "Strong representations of the Kaplan–Meier estimator and hazard estimator with censored widely orthant dependent data," Computational Statistics, Springer, vol. 37(1), pages 383-402, March.
    12. Hong-Xia Xu & Guo-Liang Fan & Zhen-Long Chen & Jiang-Feng Wang, 2018. "Weighted quantile regression and testing for varying-coefficient models with randomly truncated data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(4), pages 565-588, October.
    13. Han-Ying Liang & Jacobo Uña-Álvarez, 2011. "Asymptotic properties of conditional quantile estimator for censored dependent observations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 267-289, April.
    14. Quintela-del-Río, A., 2011. "Comparative seismic hazard analysis of two Spanish regions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2738-2748.
    15. Rachdi, Mustapha & Sabre, Rachid, 2000. "Consistent estimates of the mode of the probability density function in nonparametric deconvolution problems," Statistics & Probability Letters, Elsevier, vol. 47(2), pages 105-114, April.
    16. Kouritzin, Michael A. & Lê, Khoa & Sezer, Deniz, 2019. "Laws of large numbers for supercritical branching Gaussian processes," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3463-3498.
    17. David Atienza & Pedro Larrañaga & Concha Bielza, 2022. "Rejoinder on: Hybrid semiparametric Bayesian networks," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 31(2), pages 344-347, June.
    18. José E. Chacón, 2020. "The Modal Age of Statistics," International Statistical Review, International Statistical Institute, vol. 88(1), pages 122-141, April.
    19. Taoufik Bouezmarni & Jeroen Rombouts, 2008. "Density and hazard rate estimation for censored and α-mixing data using gamma kernels," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(7), pages 627-643.
    20. Rafael Weißbach & Wladislaw Poniatowski & Walter Krämer, 2013. "Nearest neighbor hazard estimation with left-truncated duration data," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(1), pages 33-47, January.

    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:stpapr:v:56:y:2015:i:3:p:887-910. 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.