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

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  • 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

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  • 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
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    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.
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    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.

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