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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. 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.
    3. 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.
    4. 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.
    5. Kotz,Samuel & Nadarajah,Saralees, 2004. "Multivariate T-Distributions and Their Applications," Cambridge Books, Cambridge University Press, number 9780521826549, January.
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