IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v11y2023i23p4853-d1293007.html
   My bibliography  Save this article

Estimation in Semi-Varying Coefficient Heteroscedastic Instrumental Variable Models with Missing Responses

Author

Listed:
  • Weiwei Zhang

    (College of Science, Inner Mongolia Agricultural University, Hohhot 010018, China)

  • Jingxuan Luo

    (School of Statistics, Beijing Normal University, Beijing 100875, China)

  • Shengyun Ma

    (College of Science, Inner Mongolia Agricultural University, Hohhot 010018, China)

Abstract

This paper studies the estimation problem for semi-varying coefficient heteroscedastic instrumental variable models with missing responses. First, we propose the adjusted estimators for unknown parameters and smooth functional coefficients utilizing the ordinary profile least square method and instrumental variable adjustment technique with complete data. Second, we present an adjusted estimator of the stochastic error variance by employing the Nadaraya–Watson kernel estimation technique. Third, we apply the inverse probability-weighted method and instrumental variable adjustment technique to construct the adaptive-weighted adjusted estimators for unknown parameters and smooth functional coefficients. The asymptotic properties of our proposed estimators are established under some regularity conditions. Finally, numerous simulation studies and a real data analysis are conducted to examine the finite sample performance of the proposed estimators.

Suggested Citation

  • Weiwei Zhang & Jingxuan Luo & Shengyun Ma, 2023. "Estimation in Semi-Varying Coefficient Heteroscedastic Instrumental Variable Models with Missing Responses," Mathematics, MDPI, vol. 11(23), pages 1-20, December.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:23:p:4853-:d:1293007
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/11/23/4853/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/11/23/4853/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Shi, Jian & Lau, Tai-Shing, 2000. "Empirical Likelihood for Partially Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 132-148, January.
    2. Fanrong Zhao & Weixing Song & Jianhong Shi, 2018. "Statistical inference for heteroscedastic semi-varying coefficient EV models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(10), pages 2432-2455, May.
    3. Zhao, Peixin & Xue, Liugen, 2009. "Variable selection for semiparametric varying coefficient partially linear models," Statistics & Probability Letters, Elsevier, vol. 79(20), pages 2148-2157, October.
    4. Shen, Si-Lian & Cui, Jian-Ling & Mei, Chang-Lin & Wang, Chun-Wei, 2014. "Estimation and inference of semi-varying coefficient models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 70-93.
    5. Feng Yao, 2012. "Efficient Semiparametric Instrumental Variable Estimation under Conditional Heteroskedasticity," Journal of Quantitative Economics, The Indian Econometric Society, vol. 10(1), pages 32-55, January.
    6. Zongwu Cai & Huaiyu Xiong, 2012. "Partially varying coefficient instrumental variables models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 66(2), pages 85-110, May.
    7. Jiting Huang & Peixin Zhao, 2018. "Orthogonal weighted empirical likelihood-based variable selection for semiparametric instrumental variable models," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 47(18), pages 4375-4388, September.
    8. Xinrong Tang & Peixin Zhao & Yiping Yang & Weiming Yang, 2022. "Adjusted empirical likelihood inferences for varying coefficient partially non linear models with endogenous covariates," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 51(4), pages 953-973, February.
    9. Wang Q. & Linton O. & Hardle W., 2004. "Semiparametric Regression Analysis With Missing Response at Random," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 334-345, January.
    10. Hong-Xia Xu & Guo-Liang Fan & Cheng-Xin Wu & Zhen-Long Chen, 2019. "Statistical inference for varying-coefficient partially linear errors-in-variables models with missing data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(22), pages 5621-5636, November.
    11. Yiping Yang & Lifang Chen & Peixin Zhao, 2017. "Empirical likelihood inference in partially linear single-index models with endogenous covariates," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(7), pages 3297-3307, April.
    12. Zhou, Xian & You, Jinhong, 2004. "Wavelet estimation in varying-coefficient partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 68(1), pages 91-104, June.
    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. Shen, Si-Lian & Cui, Jian-Ling & Mei, Chang-Lin & Wang, Chun-Wei, 2014. "Estimation and inference of semi-varying coefficient models with heteroscedastic errors," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 70-93.
    2. Zhao, Yan-Yong & Lin, Jin-Guan & Xu, Pei-Rong & Ye, Xu-Guo, 2015. "Orthogonality-projection-based estimation for semi-varying coefficient models with heteroscedastic errors," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 204-221.
    3. Yongsong Qin & Jianjun Li, 2011. "Empirical likelihood for partially linear models with missing responses at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(2), pages 497-511.
    4. Majid Mojirsheibani & Timothy Reese, 2017. "Kernel regression estimation for incomplete data with applications," Statistical Papers, Springer, vol. 58(1), pages 185-209, March.
    5. Fan, Guo-Liang & Liang, Han-Ying & Shen, Yu, 2016. "Penalized empirical likelihood for high-dimensional partially linear varying coefficient model with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 183-201.
    6. Dlugosz, Stephan & Mammen, Enno & Wilke, Ralf A., 2017. "Generalized partially linear regression with misclassified data and an application to labour market transitions," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 145-159.
    7. Kai Yang & Xue Ding & Xiaohui Yuan, 2022. "Bayesian empirical likelihood inference and order shrinkage for autoregressive models," Statistical Papers, Springer, vol. 63(1), pages 97-121, February.
    8. Wei Yu & Cuizhen Niu & Wangli Xu, 2014. "An empirical likelihood inference for the coefficient difference of a two-sample linear model with missing response data," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(5), pages 675-693, July.
    9. Chen, Songxi, 2012. "Estimation in semiparametric models with missing data," MPRA Paper 46216, University Library of Munich, Germany.
    10. Jaeger, Adam & Lazar, Nicole A., 2020. "Split sample empirical likelihood," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    11. Li, Yujie & Li, Gaorong & Lian, Heng & Tong, Tiejun, 2017. "Profile forward regression screening for ultra-high dimensional semiparametric varying coefficient partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 133-150.
    12. Wangli Xu & Xu Guo & Lixing Zhu, 2012. "Goodness-of-fitting for partial linear model with missing response at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 103-118.
    13. Zhaoliang Wang & Liugen Xue & Gaorong Li & Fei Lu, 2019. "Spline estimator for ultra-high dimensional partially linear varying coefficient models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 657-677, June.
    14. Nengxiang Ling & Rui Kan & Philippe Vieu & Shuyu Meng, 2019. "Semi-functional partially linear regression model with responses missing at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 39-70, January.
    15. Song Chen & Ingrid Van Keilegom, 2009. "A review on empirical likelihood methods for regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 415-447, November.
    16. Liang, Hua & Su, Haiyan & Zou, Guohua, 2008. "Confidence intervals for a common mean with missing data with applications in an AIDS study," Computational Statistics & Data Analysis, Elsevier, vol. 53(2), pages 546-553, December.
    17. 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.
    18. Xue, Liugen & Xue, Dong, 2011. "Empirical likelihood for semiparametric regression model with missing response data," Journal of Multivariate Analysis, Elsevier, vol. 102(4), pages 723-740, April.
    19. Huang, Zhensheng & Pang, Zhen, 2012. "Corrected empirical likelihood inference for right-censored partially linear single-index model," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 276-284.
    20. Qihua Wang & Tao Zhang & Wolfgang Karl Härdle, 2016. "An Extended Single-index Model with Missing Response at Random," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(4), pages 1140-1152, 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:gam:jmathe:v:11:y:2023:i:23:p:4853-:d:1293007. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.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.