IDEAS home Printed from https://ideas.repec.org/a/spt/stecon/v7y2018i4f7_4_1.html
   My bibliography  Save this article

Nonparametric Estimation of the Error Functional of a Location-Scale Model

Author

Listed:
  • Emmanuel Torsen
  • Peter N. Mwita
  • Joseph K. Mungatu

Abstract

Two estimators of the distribution of the error term are proposed based on nonparametric regression residuals; considering a heteroscadastic location-scale model where the mean and variance functions are smooth, and the error term is independent of the independent variable. The asymptotic properties of the two estimators: the unconditional cumulative distribution estimator and the conditional cumulative distribution estimator were examined. Simulation study was conducted, the mean square error of the unconditional cumulative distribution estimator was found to be smaller in comparison to its conditional cumulative distribution estimator counterpart. Hence, we recommend the use of the former.Mathematics Subject Classification: 62F05; 62M10Keywords: Nonparametric Estimation; Residuals; Error Term; Location- Scale Model

Suggested Citation

  • Emmanuel Torsen & Peter N. Mwita & Joseph K. Mungatu, 2018. "Nonparametric Estimation of the Error Functional of a Location-Scale Model," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 7(4), pages 1-1.
    • Handle: RePEc:spt:stecon:v:7:y:2018:i:4:f:7_4_1
    as

    Download full text from publisher

    File URL: http://www.scienpress.com/Upload/JSEM%2fVol%207_4_1.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Michael G. Akritas & Ingrid Van Keilegom, 2001. "Non‐parametric Estimation of the Residual Distribution," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(3), pages 549-567, September.
    2. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    3. Martins-Filho, Carlos & Yao, Feng & Torero, Maximo, 2018. "Nonparametric Estimation Of Conditional Value-At-Risk And Expected Shortfall Based On Extreme Value Theory," Econometric Theory, Cambridge University Press, vol. 34(1), pages 23-67, February.
    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. Emmanuel Torsen & Peter N. Mwita & Joseph K. Mung’atu, 2019. "A Three-Step Nonparametric Estimation of Conditional Value-At-Risk Admitting a Location-Scale Model," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(4), pages 1-1.

    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. Martins-Filho, Carlos & Yao, Feng & Torero, Maximo, 2018. "Nonparametric Estimation Of Conditional Value-At-Risk And Expected Shortfall Based On Extreme Value Theory," Econometric Theory, Cambridge University Press, vol. 34(1), pages 23-67, February.
    2. Holger Dette & Kay Pilz, 2009. "On the estimation of a monotone conditional variance in nonparametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 111-141, March.
    3. Dingshi Tian & Zongwu Cai & Ying Fang, 2018. "Econometric Modeling of Risk Measures: A Selective Review of the Recent Literature," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201807, University of Kansas, Department of Economics, revised Oct 2018.
    4. Emmanuel Torsen & Peter N. Mwita & Joseph K. Mung’atu, 2019. "A Three-Step Nonparametric Estimation of Conditional Value-At-Risk Admitting a Location-Scale Model," Journal of Statistical and Econometric Methods, SCIENPRESS Ltd, vol. 8(4), pages 1-1.
    5. Dette, Holger & Pilz, Kay F., 2004. "On the estimation of a monotone conditional variance in nonparametric regression," Technical Reports 2004,42, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    6. Hoderlein, Stefan & White, Halbert, 2012. "Nonparametric identification in nonseparable panel data models with generalized fixed effects," Journal of Econometrics, Elsevier, vol. 168(2), pages 300-314.
    7. Jing Lv & Chaohui Guo, 2017. "Efficient parameter estimation via modified Cholesky decomposition for quantile regression with longitudinal data," Computational Statistics, Springer, vol. 32(3), pages 947-975, September.
    8. Yanchun Jin, 2016. "Nonparametric tests for the effect of treatment on conditional variance," KIER Working Papers 948, Kyoto University, Institute of Economic Research.
    9. Xingcai Zhou & Dehan Kong & Matthew Stephen Pietrosanu & Linglong Kong & Rohana J. Karunamuni, 2024. "Empirical likelihood M‐estimation for the varying‐coefficient model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 51(3), pages 1357-1387, September.
    10. Otsu, Taisuke & Xu, Ke-Li & Matsushita, Yukitoshi, 2015. "Empirical likelihood for regression discontinuity design," Journal of Econometrics, Elsevier, vol. 186(1), pages 94-112.
    11. Heather L. R. Tierney, 2019. "Forecasting with the Nonparametric Exclusion-from-Core Inflation Persistence Model Using Real-Time Data," International Advances in Economic Research, Springer;International Atlantic Economic Society, vol. 25(1), pages 39-63, February.
    12. Holger Dette & Mareen Marchlewski & Jens Wagener, 2012. "Testing for a constant coefficient of variation in nonparametric regression by empirical processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 1045-1070, October.
    13. Tran, Kien C. & Tsionas, Efthymios G., 2009. "Estimation of nonparametric inefficiency effects stochastic frontier models with an application to British manufacturing," Economic Modelling, Elsevier, vol. 26(5), pages 904-909, September.
    14. León Beleña & Ernesto Curbelo & Luca Martino & Valero Laparra, 2024. "Second-Moment/Order Approximations by Kernel Smoothers with Application to Volatility Estimation," Mathematics, MDPI, vol. 12(9), pages 1-15, May.
    15. Santos, Douglas G. & Candido, Osvaldo & Tófoli, Paula V., 2022. "Forecasting risk measures using intraday and overnight information," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    16. Einmahl, John H.J. & Van Keilegom, Ingrid, 2008. "Specification tests in nonparametric regression," Journal of Econometrics, Elsevier, vol. 143(1), pages 88-102, March.
    17. Feve, Frederique & Florens, Jean-Pierre & Van Keilegom, Ingrid, 2012. "Estimation of conditional ranks and tests of exogeneity in nonparametric nonseparable models," LIDAM Discussion Papers ISBA 2012036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    18. Gao, Jiti & King, Maxwell, 2003. "Estimation and model specification testing in nonparametric and semiparametric econometric models," MPRA Paper 11989, University Library of Munich, Germany, revised Feb 2006.
    19. Gao, Jiti & Gijbels, Irene & Van Bellegem, Sebastien, 2008. "Nonparametric simultaneous testing for structural breaks," Journal of Econometrics, Elsevier, vol. 143(1), pages 123-142, March.
    20. Čížek, Pavel & Koo, Chao Hui, 2021. "Jump-preserving varying-coefficient models for nonlinear time series," Econometrics and Statistics, Elsevier, vol. 19(C), pages 58-96.

    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:spt:stecon:v:7:y:2018:i:4:f:7_4_1. 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: Eleftherios Spyromitros-Xioufis (email available below). General contact details of provider: http://www.scienpress.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.