IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v71y2019i1d10.1007_s10463-017-0622-0.html
   My bibliography  Save this article

Semiparametric efficient estimators in heteroscedastic error models

Author

Listed:
  • Mijeong Kim

    (Ewha Womans University)

  • Yanyuan Ma

    (Penn State University)

Abstract

In the mean regression context, this study considers several frequently encountered heteroscedastic error models where the regression mean and variance functions are specified up to certain parameters. An important point we note through a series of analyses is that different assumptions on standardized regression errors yield quite different efficiency bounds for the corresponding estimators. Consequently, all aspects of the assumptions need to be specifically taken into account in constructing their corresponding efficient estimators. This study clarifies the relation between the regression error assumptions and their, respectively, efficiency bounds under the general regression framework with heteroscedastic errors. Our simulation results support our findings; we carry out a real data analysis using the proposed methods where the Cobb–Douglas cost model is the regression mean.

Suggested Citation

  • Mijeong Kim & Yanyuan Ma, 2019. "Semiparametric efficient estimators in heteroscedastic error models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(1), pages 1-28, February.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:1:d:10.1007_s10463-017-0622-0
    DOI: 10.1007/s10463-017-0622-0
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10463-017-0622-0
    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/s10463-017-0622-0?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. Heng Lian & Hua Liang & Raymond J. Carroll, 2015. "Variance function partially linear single-index models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 77(1), pages 171-194, January.
    2. Yanyuan Ma & Jeng-Min Chiou & Naisyin Wang, 2006. "Efficient semiparametric estimator for heteroscedastic partially linear models," Biometrika, Biometrika Trust, vol. 93(1), pages 75-84, March.
    3. Saralees Nadarajah, 2005. "A generalized normal distribution," Journal of Applied Statistics, Taylor & Francis Journals, vol. 32(7), pages 685-694.
    4. Mijeong Kim & Yanyuan Ma, 2012. "The efficiency of the second-order nonlinear least squares estimator and its extension," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 751-764, 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. Weibin Mo & Yufeng Liu, 2022. "Efficient learning of optimal individualized treatment rules for heteroscedastic or misspecified treatment‐free effect models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(2), pages 440-472, April.
    2. Yixin Fang & Heng Lian & Hua Liang, 2018. "A generalized partially linear framework for variance functions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1147-1175, October.
    3. Zhou, Ling & Lin, Huazhen & Chen, Kani & Liang, Hua, 2019. "Efficient estimation and computation of parameters and nonparametric functions in generalized semi/non-parametric regression models," Journal of Econometrics, Elsevier, vol. 213(2), pages 593-607.
    4. García, V.J. & Gómez-Déniz, E. & Vázquez-Polo, F.J., 2010. "A new skew generalization of the normal distribution: Properties and applications," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 2021-2034, August.
    5. Jun Zhang, 2021. "Estimation and variable selection for partial linear single-index distortion measurement errors models," Statistical Papers, Springer, vol. 62(2), pages 887-913, April.
    6. Müller K. & Richter W.-D., 2016. "Exact distributions of order statistics of dependent random variables from ln,p-symmetric sample distributions, n ∈ {3,4}," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-29, February.
    7. Sandi Baressi Šegota & Nikola Anđelić & Mario Šercer & Hrvoje Meštrić, 2022. "Dynamics Modeling of Industrial Robotic Manipulators: A Machine Learning Approach Based on Synthetic Data," Mathematics, MDPI, vol. 10(7), pages 1-17, April.
    8. Xin Chen & Zhangming Shan & Decai Tang & Biao Zhou & Valentina Boamah, 2023. "Interest rate risk of Chinese commercial banks based on the GARCH-EVT model," Palgrave Communications, Palgrave Macmillan, vol. 10(1), pages 1-11, December.
    9. Jeong, Hanbat & Lee, Lung-fei, 2024. "Maximum likelihood estimation of a spatial autoregressive model for origin–destination flow variables," Journal of Econometrics, Elsevier, vol. 242(1).
    10. Runze Li & Lei Nie, 2008. "Efficient Statistical Inference Procedures for Partially Nonlinear Models and their Applications," Biometrics, The International Biometric Society, vol. 64(3), pages 904-911, September.
    11. Kapla, Daniel & Fertl, Lukas & Bura, Efstathia, 2022. "Fusing sufficient dimension reduction with neural networks," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    12. Lassance, Nathan & Vrins, Frédéric, 2023. "Portfolio selection: A target-distribution approach," European Journal of Operational Research, Elsevier, vol. 310(1), pages 302-314.
    13. Lai, Peng & Wang, Qihua & Zhou, Xiao-Hua, 2014. "Variable selection and semiparametric efficient estimation for the heteroscedastic partially linear single-index model," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 241-256.
    14. Otsu, Taisuke, 2007. "Penalized empirical likelihood estimation of semiparametric models," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1923-1954, November.
    15. Wang, Xiaoguang & Lu, Dawei & Song, Lixin, 2013. "Statistical inference for partially linear stochastic models with heteroscedastic errors," Computational Statistics & Data Analysis, Elsevier, vol. 66(C), pages 150-160.
    16. Lu, Xuewen, 2009. "Empirical likelihood for heteroscedastic partially linear models," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 387-396, March.
    17. Hohsuk Noh & Seong J. Yang, 2020. "Comparing Groups of Decision-Making Units in Efficiency Based on Semiparametric Regression," Mathematics, MDPI, vol. 8(2), pages 1-16, February.
    18. Tran, Quang Van & Kukal, Jaromir, 2022. "A novel heavy tail distribution of logarithmic returns of cryptocurrencies," Finance Research Letters, Elsevier, vol. 47(PA).
    19. Tang, Niansheng & Xia, Linli & Yan, Xiaodong, 2019. "Feature screening in ultrahigh-dimensional partially linear models with missing responses at random," Computational Statistics & Data Analysis, Elsevier, vol. 133(C), pages 208-227.
    20. Jayles, Bertrand & Escobedo, Ramon & Cezera, Stéphane & Blanchet, Adrien & Kameda, Tatsuya & Sire, Clément & Théraulaz, Guy, 2020. "The impact of incorrect social information on collective wisdom in human groups," IAST Working Papers 20-106, Institute for Advanced Study in Toulouse (IAST).

    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:aistmt:v:71:y:2019:i:1:d:10.1007_s10463-017-0622-0. 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.