IDEAS home Printed from https://ideas.repec.org/a/spr/sankhb/v81y2019i1d10.1007_s13571-019-00189-8.html
   My bibliography  Save this article

The Second-Order Asymptotic Properties of Asymmetric Least Squares Estimation

Author

Listed:
  • Tae-Hwy Lee

    (University of California)

  • Aman Ullah

    (University of California)

  • He Wang

    (University of California)

Abstract

The higher-order asymptotic properties provide better approximation of the bias for a class of estimators. The first-order asymptotic properties of the asymmetric least squares (ALS) estimator have been investigated by Newey and Powell (Econometrica55, 4, 819–847 1987). This paper develops the second-order asymptotic properties (bias and mean squared error) of the ALS estimator, extending the second-order asymptotic results for the symmetric least squares (LS) estimators of Rilstone et al. (J. Econometr.75, 369–395 1996). The LS gives the mean regression function while the ALS gives the “expectile” regression function, a generalization of the usual regression function. The second-order bias result enables an improved bias correction and thus an improved ALS estimation in finite sample. In particular, we show that the second-order bias is much larger as the asymmetry is stronger, and therefore the benefit of the second-order bias correction is greater when we are interested in extreme expectiles which are used as a risk measure in financial economics. The higher-order MSE result for the ALS estimation also enables us to better understand the sources of estimation uncertainty. The Monte Carlo simulation confirms the benefits of the second-order asymptotic theory and indicates that the second-order bias is larger at the extreme low and high expectiles.

Suggested Citation

  • Tae-Hwy Lee & Aman Ullah & He Wang, 2019. "The Second-Order Asymptotic Properties of Asymmetric Least Squares Estimation," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 201-233, September.
    • Handle: RePEc:spr:sankhb:v:81:y:2019:i:1:d:10.1007_s13571-019-00189-8
    DOI: 10.1007/s13571-019-00189-8
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13571-019-00189-8
    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/s13571-019-00189-8?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 look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kuan, Chung-Ming & Yeh, Jin-Huei & Hsu, Yu-Chin, 2009. "Assessing value at risk with CARE, the Conditional Autoregressive Expectile models," Journal of Econometrics, Elsevier, vol. 150(2), pages 261-270, June.
    2. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643, September.
    3. Bao, Yong & Ullah, Aman, 2007. "The second-order bias and mean squared error of estimators in time-series models," Journal of Econometrics, Elsevier, vol. 140(2), pages 650-669, October.
    4. Yao, Qiwei & Tong, Howell, 1996. "Asymmetric least squares regression estimation: a nonparametric approach," LSE Research Online Documents on Economics 19423, London School of Economics and Political Science, LSE Library.
    5. Rilstone, Paul & Srivastava, V. K. & Ullah, Aman, 1996. "The second-order bias and mean squared error of nonlinear estimators," Journal of Econometrics, Elsevier, vol. 75(2), pages 369-395, December.
    6. Aigner, D J & Amemiya, Takeshi & Poirier, Dale J, 1976. "On the Estimation of Production Frontiers: Maximum Likelihood Estimation of the Parameters of a Discontinuous Density Function," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 377-396, June.
    7. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    8. Shangyu Xie & Yong Zhou & Alan T. K. Wan, 2014. "A Varying-Coefficient Expectile Model for Estimating Value at Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 576-592, October.
    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. Arnab Bhattacharjee & Tapabrata Maiti, 2019. "P. C. Mahalanobis in the Context of Current Econometrics Research," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 1-11, September.

    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. Zhang, Feipeng & Li, Qunhua, 2017. "A continuous threshold expectile model," Computational Statistics & Data Analysis, Elsevier, vol. 116(C), pages 49-66.
    2. Yundong Tu & Siwei Wang, 2023. "Variable Screening and Model Averaging for Expectile Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 85(3), pages 574-598, June.
    3. Zhang, Feipeng & Xu, Yixiong & Fan, Caiyun, 2023. "Nonparametric inference of expectile-based value-at-risk for financial time series with application to risk assessment," International Review of Financial Analysis, Elsevier, vol. 90(C).
    4. Xiu Xu & Andrija Mihoci & Wolfgang Karl Hardle, 2020. "lCARE -- localizing Conditional AutoRegressive Expectiles," Papers 2009.13215, arXiv.org.
    5. Xu, Xiu & Mihoci, Andrija & Härdle, Wolfgang Karl, 2018. "lCARE - localizing conditional autoregressive expectiles," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 198-220.
    6. Man, Rebeka & Tan, Kean Ming & Wang, Zian & Zhou, Wen-Xin, 2024. "Retire: Robust expectile regression in high dimensions," Journal of Econometrics, Elsevier, vol. 239(2).
    7. Yao, Yinhong & Li, Jianping & Sun, Xiaolei, 2021. "Measuring the risk of Chinese Fintech industry: evidence from the stock index," Finance Research Letters, Elsevier, vol. 39(C).
    8. Zhang, Yue-Jun & Ma, Shu-Jiao, 2019. "How to effectively estimate the time-varying risk spillover between crude oil and stock markets? Evidence from the expectile perspective," Energy Economics, Elsevier, vol. 84(C).
    9. Garcia-Jorcano, Laura & Sanchis-Marco, Lidia, 2022. "Spillover effects between commodity and stock markets: A SDSES approach," Resources Policy, Elsevier, vol. 79(C).
    10. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    11. repec:hum:wpaper:sfb649dp2015-052 is not listed on IDEAS
    12. Shangyu Xie & Yong Zhou & Alan T. K. Wan, 2014. "A Varying-Coefficient Expectile Model for Estimating Value at Risk," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(4), pages 576-592, October.
    13. Antonio Rubia Serrano & Lidia Sanchis-Marco, 2015. "Measuring Tail-Risk Cross-Country Exposures in the Banking Industry," Working Papers. Serie AD 2015-01, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
    14. Zongwu Cai & Ying Fang & Dingshi Tian, 2018. "Assessing Tail Risk Using Expectile Regressions with Partially Varying Coefficients," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201804, University of Kansas, Department of Economics, revised Oct 2018.
    15. Taoufik Bouezmarni & Mohamed Doukali & Abderrahim Taamouti, 2024. "Testing Granger non-causality in expectiles," Econometric Reviews, Taylor & Francis Journals, vol. 43(1), pages 30-51, January.
    16. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    17. Daouia, Abdelaati & Paindaveine, Davy, 2019. "Multivariate Expectiles, Expectile Depth and Multiple-Output Expectile Regression," TSE Working Papers 19-1022, Toulouse School of Economics (TSE), revised Feb 2023.
    18. Hamidi, Benjamin & Maillet, Bertrand & Prigent, Jean-Luc, 2014. "A dynamic autoregressive expectile for time-invariant portfolio protection strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 46(C), pages 1-29.
    19. Busetti, Fabio & Caivano, Michele & Delle Monache, Davide & Pacella, Claudia, 2021. "The time-varying risk of Italian GDP," Economic Modelling, Elsevier, vol. 101(C).
    20. repec:dau:papers:123456789/15232 is not listed on IDEAS
    21. Wang, Bingling & Li, Yingxing & Härdle, Wolfgang Karl, 2022. "K-expectiles clustering," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    22. Lina Liao & Cheolwoo Park & Hosik Choi, 2019. "Penalized expectile regression: an alternative to penalized quantile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(2), pages 409-438, April.

    More about this item

    Keywords

    Asymmetric least squares; Expectile; Delta function; Second-order bias; Monte Carlo.;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    Statistics

    Access and download statistics

    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:sankhb:v:81:y:2019:i:1:d:10.1007_s13571-019-00189-8. 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.