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Asymptotics for the nonparametric estimation of the mean function of a random process

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  • Degras, David

Abstract

We study the nonparametric estimation of the mean function of a random process indexed by a compact metric space. We elaborate on the asymptotic variance and prove asymptotic normality for a general class of linear estimators. An application to simultaneous confidence intervals is proposed and investigated by simulation.

Suggested Citation

  • Degras, David, 2008. "Asymptotics for the nonparametric estimation of the mean function of a random process," Statistics & Probability Letters, Elsevier, vol. 78(17), pages 2976-2980, December.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:17:p:2976-2980
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    References listed on IDEAS

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    1. Anilkumar, P., 1994. "On estimating the mean function of a Gaussian process," Statistics & Probability Letters, Elsevier, vol. 19(1), pages 77-84, January.
    2. Wei Biao Wu & Zhibiao Zhao, 2007. "Inference of trends in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 391-410, June.
    3. Minggen Lu & Ying Zhang & Jian Huang, 2007. "Estimation of the mean function with panel count data using monotone polynomial splines," Biometrika, Biometrika Trust, vol. 94(3), pages 705-718.
    4. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, November.
    5. Yao, Fang, 2007. "Asymptotic distributions of nonparametric regression estimators for longitudinal or functional data," Journal of Multivariate Analysis, Elsevier, vol. 98(1), pages 40-56, January.
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