IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v61y2020i3d10.1007_s00362-018-0983-3.html
   My bibliography  Save this article

Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models

Author

Listed:
  • Xuejun Wang

    (Anhui University)

  • Yi Wu

    (Anhui University)

  • Shuhe Hu

    (Anhui University)

  • Nengxiang Ling

    (Hefei University of Technology)

Abstract

In this paper, a general result on complete moment convergence for arrays of rowwise negatively orthant dependent random variables is obtained. In addition, we present some sufficient conditions to prove the complete moment and complete convergences for the variables. As applications, the complete consistency for the estimators of nonparametric and semiparametric regression models based on negatively orthant dependent errors is established by using the complete convergence that we established. A simulation to study the numerical performance of the consistency for the nearest neighbor weight function estimator in semiparametric regression model is given. Our results generalize and improve some corresponding ones for independent random variables and negatively associated random variables.

Suggested Citation

  • Xuejun Wang & Yi Wu & Shuhe Hu & Nengxiang Ling, 2020. "Complete moment convergence for negatively orthant dependent random variables and its applications in statistical models," Statistical Papers, Springer, vol. 61(3), pages 1147-1180, June.
    • Handle: RePEc:spr:stpapr:v:61:y:2020:i:3:d:10.1007_s00362-018-0983-3
    DOI: 10.1007/s00362-018-0983-3
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-018-0983-3
    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/s00362-018-0983-3?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. Aiting Shen & Ying Zhang & Andrei Volodin, 2015. "Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 295-311, April.
    2. Xuejun Wang & Fengxi Xia & Meimei Ge & Shuhe Hu & Wenzhi Yang, 2012. "Complete Consistency of the Estimator of Nonparametric Regression Models Based on -Mixing Sequences," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-12, December.
    3. Wang, Xuejun & Hu, Shuhe & Yang, Wenzhi & Ling, Nengxiang, 2010. "Exponential inequalities and inverse moment for NOD sequence," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 452-461, March.
    4. Fan, Y., 1990. "Consistent nonparametric multiple regression for dependent heterogeneous processes: The fixed design case," Journal of Multivariate Analysis, Elsevier, vol. 33(1), pages 72-88, April.
    5. Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
    6. Georgiev, Alexander A., 1988. "Consistent nonparametric multiple regression: The fixed design case," Journal of Multivariate Analysis, Elsevier, vol. 25(1), pages 100-110, April.
    7. H. Zarei & H. Jabbari, 2011. "Complete convergence of weighted sums under negative dependence," Statistical Papers, Springer, vol. 52(2), pages 413-418, May.
    8. Zhou, Xing-cai & Lin, Jin-guan, 2013. "Asymptotic properties of wavelet estimators in semiparametric regression models under dependent errors," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 251-270.
    9. Roussas, George G., 1989. "Consistent regression estimation with fixed design points under dependence conditions," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 41-50, May.
    10. Soo Sung, 2012. "Complete convergence for weighted sums of negatively dependent random variables," Statistical Papers, Springer, vol. 53(1), pages 73-82, February.
    11. Liang, Han-Ying & Jing, Bing-Yi, 2005. "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 227-245, August.
    12. Qunying Wu, 2011. "Complete Convergence for Weighted Sums of Sequences of Negatively Dependent Random Variables," Journal of Probability and Statistics, Hindawi, vol. 2011, pages 1-16, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Nan Cheng & Chao Lu & Jibing Qi & Xuejun Wang, 2022. "Complete moment convergence for randomly weighted sums of extended negatively dependent random variables with application to semiparametric regression models," Statistical Papers, Springer, vol. 63(2), pages 397-419, April.

    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. Xuejun Wang & Zeyu Si, 2015. "Complete consistency of the estimator of nonparametric regression model under ND sequence," Statistical Papers, Springer, vol. 56(3), pages 585-596, August.
    2. Xuejun Wang & Yi Wu & Shuhe Hu, 2019. "The Berry–Esseen bounds of the weighted estimator in a nonparametric regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(5), pages 1143-1162, October.
    3. Xuejun Wang & Chen Xu & Tien-Chung Hu & Andrei Volodin & Shuhe Hu, 2014. "On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 23(3), pages 607-629, September.
    4. Xuejun Wang & Yi Wu & Shuhe Hu, 2016. "Exponential probability inequality for $$m$$ m -END random variables and its applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 127-147, February.
    5. Wenzhi Yang & Haiyun Xu & Ling Chen & Shuhe Hu, 2018. "Complete consistency of estimators for regression models based on extended negatively dependent errors," Statistical Papers, Springer, vol. 59(2), pages 449-465, June.
    6. Aiting Shen & Ying Zhang & Andrei Volodin, 2015. "Applications of the Rosenthal-type inequality for negatively superadditive dependent random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(3), pages 295-311, April.
    7. Aiting Shen & Siyao Zhang, 2021. "On Complete Consistency for the Estimator of Nonparametric Regression Model Based on Asymptotically Almost Negatively Associated Errors," Methodology and Computing in Applied Probability, Springer, vol. 23(4), pages 1285-1307, December.
    8. Yi Wu & Xuejun Wang & Shuhe Hu & Lianqiang Yang, 2018. "Weighted version of strong law of large numbers for a class of random variables and its applications," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 379-406, June.
    9. Yi Wu & Xuejun Wang & Aiting Shen, 2021. "Strong convergence properties for weighted sums of m-asymptotic negatively associated random variables and statistical applications," Statistical Papers, Springer, vol. 62(5), pages 2169-2194, October.
    10. Xuejun Wang & Yi Wu & Rui Wang & Shuhe Hu, 2021. "On consistency of wavelet estimator in nonparametric regression models," Statistical Papers, Springer, vol. 62(2), pages 935-962, April.
    11. Yan, Ji Gao, 2018. "On Complete Convergence in Marcinkiewicz-Zygmund Type SLLN for END Random Variables and its Applications," IRTG 1792 Discussion Papers 2018-042, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    12. Wu, Yi & Wang, Xuejun & Hu, Shuhe, 2017. "Complete moment convergence for weighted sums of weakly dependent random variables and its application in nonparametric regression model," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 56-66.
    13. Zhou, Xing-cai & Lin, Jin-guan, 2012. "A wavelet estimator in a nonparametric regression model with repeated measurements under martingale difference error’s structure," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1914-1922.
    14. Yi Wu & Xuejun Wang & Aiting Shen, 2023. "Strong Convergence for Weighted Sums of Widely Orthant Dependent Random Variables and Applications," Methodology and Computing in Applied Probability, Springer, vol. 25(1), pages 1-28, March.
    15. Yang, Shanchao, 2003. "Uniformly asymptotic normality of the regression weighted estimator for negatively associated samples," Statistics & Probability Letters, Elsevier, vol. 62(2), pages 101-110, April.
    16. Aiting Shen & Andrei Volodin, 2017. "Weak and strong laws of large numbers for arrays of rowwise END random variables and their applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 605-625, November.
    17. Liang, Han-Ying & Jing, Bing-Yi, 2005. "Asymptotic properties for estimates of nonparametric regression models based on negatively associated sequences," Journal of Multivariate Analysis, Elsevier, vol. 95(2), pages 227-245, August.
    18. Han-Ying Liang & Ya-Mei Liu, 2011. "Asymptotic normality of variance estimator in a heteroscedastic model with dependent errors," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 351-365.
    19. Xin Deng & Xuejun Wang & Yi Wu, 2021. "The Berry–Esseen type bounds of the weighted estimator in a nonparametric model with linear process errors," Statistical Papers, Springer, vol. 62(2), pages 963-984, April.
    20. Liwang Ding & Ping Chen & Yongming Li, 2020. "Consistency for wavelet estimator in nonparametric regression model with extended negatively dependent samples," Statistical Papers, Springer, vol. 61(6), pages 2331-2349, December.

    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:61:y:2020:i:3:d:10.1007_s00362-018-0983-3. 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.