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Nonparametric variance function estimation with missing data

Author

Listed:
  • Pérez-González, A.
  • Vilar-Fernández, J.M.
  • González-Manteiga, W.

Abstract

In this paper, a fixed design regression model where the errors follow a strictly stationary process is considered. In this model the conditional mean function and the conditional variance function are unknown curves. Correlated errors when observations are missing in the response variable are assumed. Four nonparametric estimators of the conditional variance function based on local polynomial fitting are proposed. Expressions of the asymptotic bias and variance of these estimators are obtained. A simulation study illustrates the behavior of the proposed estimators.

Suggested Citation

  • Pérez-González, A. & Vilar-Fernández, J.M. & González-Manteiga, W., 2010. "Nonparametric variance function estimation with missing data," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1123-1142, May.
  • Handle: RePEc:eee:jmvana:v:101:y:2010:i:5:p:1123-1142
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    References listed on IDEAS

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    3. Gonzalez Manteiga, W. & Martinez Miranda, M. D. & Perez Gonzalez, A., 2004. "The choice of smoothing parameter in nonparametric regression through Wild Bootstrap," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 487-515, October.
    4. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    5. A. Pérez-González & J. Vilar-Fernández & W. González-Manteiga, 2009. "Asymptotic properties of local polynomial regression with missing data and correlated errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 85-109, March.
    6. Ziegelmann, Flavio A., 2002. "Nonparametric Estimation Of Volatility Functions: The Local Exponential Estimator," Econometric Theory, Cambridge University Press, vol. 18(04), pages 985-991, August.
    7. Yu, K. & Jones, M.C., 2004. "Likelihood-Based Local Linear Estimation of the Conditional Variance Function," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 139-144, January.
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    9. 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.
    10. Shephard, Neil (ed.), 2005. "Stochastic Volatility: Selected Readings," OUP Catalogue, Oxford University Press, number 9780199257201.
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