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Marginal nonparametric kernel regression accounting for within-subject correlation

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  • Naisyin Wang
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    Abstract

    There has been substantial recent interest in non- and semiparametric methods for longitudinal or clustered data with dependence within clusters. It has been shown rather inexplicably that, when standard kernel smoothing methods are used in a natural way, higher efficiency is obtained by assuming independence than by using the true correlation structure. It is shown here that this result is a natural consequence of how standard kernel methods incorporate the within-subject correlation in the asymptotic setting considered, where the cluster sizes are fixed and the cluster number increases. In this paper, an alternative kernel smoothing method is proposed. Unlike the standard methods, the smallest variance of the new estimator is achieved when the true correlation is assumed. Asymptotically, the variance of the proposed method is uniformly smaller than that of the most efficient working independence approach. A small simulation study shows that significant improvement is obtained for finite samples. Copyright Biometrika Trust 2003, Oxford University Press.

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    Bibliographic Info

    Article provided by Biometrika Trust in its journal Biometrika.

    Volume (Year): 90 (2003)
    Issue (Month): 1 (March)
    Pages: 43-52

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    Handle: RePEc:oup:biomet:v:90:y:2003:i:1:p:43-52

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    Cited by:
    1. Qian, Junhui & Wang, Le, 2012. "Estimating semiparametric panel data models by marginal integration," Journal of Econometrics, Elsevier, vol. 167(2), pages 483-493.
    2. Yi, Grace Y. & He, Wenqing & Liang, Hua, 2009. "Analysis of correlated binary data under partially linear single-index logistic models," Journal of Multivariate Analysis, Elsevier, vol. 100(2), pages 278-290, February.
    3. Tomasz Gerard Czekaj & Arne Henningsen, 2012. "Comparing Parametric and Nonparametric Regression Methods for Panel Data: the Optimal Size of Polish Crop Farms," IFRO Working Paper 2012/12, University of Copenhagen, Department of Food and Resource Economics.
    4. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    5. Daniel J. Henderson, 2010. "A test for multimodality of regression derivatives with application to nonparametric growth regressions," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(3), pages 458-480.
    6. Qingming Zou & Zhongyi Zhu, 2014. "M-estimators for single-index model using B-spline," Metrika, Springer, vol. 77(2), pages 225-246, February.
    7. Ke Yang, 2013. "An Improved Local-linear Estimator For Nonparametric Regression With Autoregressive Errors," Economics Bulletin, AccessEcon, vol. 33(1), pages 19-27.
    8. You, Jinhong & Zhou, Haibo, 2007. "Two-stage efficient estimation of longitudinal nonparametric additive models," Statistics & Probability Letters, Elsevier, vol. 77(17), pages 1666-1675, November.
    9. Xu, Peirong & Zhu, Lixing, 2012. "Estimation for a marginal generalized single-index longitudinal model," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 285-299.
    10. Grace Yi & Wenqing He & Hua Liang, 2011. "Semiparametric marginal and association regression methods for clustered binary data," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(3), pages 511-533, June.
    11. Martins-Filho, Carlos & Yao, Feng, 2009. "Nonparametric regression estimation with general parametric error covariance," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 309-333, March.
    12. Xueying Zheng & Wing Fung & Zhongyi Zhu, 2013. "Robust estimation in joint mean–covariance regression model for longitudinal data," Annals of the Institute of Statistical Mathematics, Springer, vol. 65(4), pages 617-638, August.
    13. Huggins, Richard, 2004. "A note on nonparametric estimation for clustered data," Statistics & Probability Letters, Elsevier, vol. 69(2), pages 129-133, August.
    14. Al Kadiri, M. & Carroll, R.J. & Wand, M.P., 2010. "Marginal longitudinal semiparametric regression via penalized splines," Statistics & Probability Letters, Elsevier, vol. 80(15-16), pages 1242-1252, August.
    15. Li, Jialiang & Xia, Yingcun & Palta, Mari & Shankar, Anoop, 2009. "Impact of unknown covariance structures in semiparametric models for longitudinal data: An application to Wisconsin diabetes data," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4186-4197, October.
    16. Li, Lexin & Yin, Xiangrong, 2009. "Longitudinal data analysis using sufficient dimension reduction method," Computational Statistics & Data Analysis, Elsevier, vol. 53(12), pages 4106-4115, October.
    17. Lena Korber & Oliver Linton & Michael Vogt, 2013. "A semiparametric model for heterogeneous panel data with fixed effects," CeMMAP working papers CWP02/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Henderson, Daniel J. & Carroll, Raymond J. & Li, Qi, 2008. "Nonparametric estimation and testing of fixed effects panel data models," Journal of Econometrics, Elsevier, vol. 144(1), pages 257-275, May.

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