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Profile-kernel versus backfitting in the partially linear models for longitudinal/clustered data

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  • Zonghui Hu

Abstract

We study the profile-kernel and backfitting methods in partially linear models for clustered/longitudinal data. For independent data, despite the potential root-n inconsistency of the backfitting estimator noted by Rice (1986), the two estimators have the same asymptotic variance matrix, as shown by Opsomer & Ruppert (1999). In this paper, theoretical comparisons of the two estimators for multivariate responses are investigated. We show that, for correlated data, backfitting often produces a larger asymptotic variance than the profile-kernel method; that is, for clustered data, in addition to its bias problem, the backfitting estimator does not have the same asymptotic efficiency as the profile-kernel estimator. Consequently, the common practice of using the backfitting method to compute profile-kernel estimates is no longer advised. We illustrate this in detail by following Zeger & Diggle (1994) and Lin & Carroll (2001) with a working independence covariance structure for nonparametric estimation and a correlated covariance structure for parametric estimation. Numerical performance of the two estimators is investigated through a simulation study. Their application to an ophthalmology dataset is also described. Copyright Biometrika Trust 2004, Oxford University Press.

Suggested Citation

  • Zonghui Hu, 2004. "Profile-kernel versus backfitting in the partially linear models for longitudinal/clustered data," Biometrika, Biometrika Trust, vol. 91(2), pages 251-262, June.
    • Handle: RePEc:oup:biomet:v:91:y:2004:i:2:p:251-262
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    Cited by:

    1. M. Taavoni & M. Arashi, 2021. "Kernel estimation in semiparametric mixed effect longitudinal modeling," Statistical Papers, Springer, vol. 62(3), pages 1095-1116, June.
    2. Runze Li & Lei Nie, 2008. "Efficient Statistical Inference Procedures for Partially Nonlinear Models and their Applications," Biometrics, The International Biometric Society, vol. 64(3), pages 904-911, September.
    3. Colin Wu & Xin Tian & Jarvis Yu, 2010. "Nonparametric estimation for time-varying transformation models with longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(2), pages 133-147.
    4. Chen, Huaihou & Paik, Myunghee Cho & Dhamoon, Mandip S. & Moon, Yeseon Park & Willey, Joshua & Sacco, Ralph L. & Elkind, Mitchell S.V., 2012. "Semiparametric model for the dichotomized functional outcome after stroke: The Northern Manhattan Study," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2598-2608.
    5. Lam, Clifford & Fan, Jianqing, 2008. "Profile-kernel likelihood inference with diverging number of parameters," LSE Research Online Documents on Economics 31548, London School of Economics and Political Science, LSE Library.
    6. 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.
    7. Mohammed Chowdhury & Colin Wu & Reza Modarres, 2018. "Nonparametric estimation of conditional distribution functions with longitudinal data and time-varying parametric models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(1), pages 61-83, January.
    8. Su, Liangjun & Ullah, Aman, 2006. "Profile likelihood estimation of partially linear panel data models with fixed effects," Economics Letters, Elsevier, vol. 92(1), pages 75-81, July.
    9. Wang, Qihua & Sun, Zhihua, 2007. "Estimation in partially linear models with missing responses at random," Journal of Multivariate Analysis, Elsevier, vol. 98(7), pages 1470-1493, August.
    10. Zhang, Jun & Lin, Bingqing & Zhou, Yan, 2021. "Kernel density estimation for partial linear multivariate responses models," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    11. Lei Liu & Zhihua Sun, 2017. "Kernel-based global MLE of partial linear random effects models for longitudinal data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(3), pages 615-635, July.
    12. Yanqing Sun & Qiong Shou & Peter B. Gilbert & Fei Heng & Xiyuan Qian, 2023. "Semiparametric additive time‐varying coefficients model for longitudinal data with censored time origin," Biometrics, The International Biometric Society, vol. 79(2), pages 695-710, June.

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