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Optimal asymptotic MSE of kernel regression estimate for continuous time processes with missing at random response

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  • Chaouch, Mohamed
  • Laïb, Naâmane

Abstract

Based on an incomplete observed sample (Xt,Yt,ζt)0≤t≤T, where ζt=1 if Yt is observed at time t and ζt=0 otherwise, the asymptotic mean square error of the regression estimator m̂T(x),x∈Rd, is showed to satisfy the following inequality: limT→∞T4∕(d+4)E(m̂T(x)−m(x))2

Suggested Citation

  • Chaouch, Mohamed & Laïb, Naâmane, 2019. "Optimal asymptotic MSE of kernel regression estimate for continuous time processes with missing at random response," Statistics & Probability Letters, Elsevier, vol. 154(C), pages 1-1.
    • Handle: RePEc:eee:stapro:v:154:y:2019:i:c:18
    DOI: 10.1016/j.spl.2019.06.008
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    References listed on IDEAS

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    1. Didi, Sultana & Louani, Djamal, 2013. "Consistency results for the kernel density estimate on continuous time stationary and dependent data," Statistics & Probability Letters, Elsevier, vol. 83(4), pages 1262-1270.
    2. El Heda, Khadijetou & Louani, Djamal, 2018. "Optimal bandwidth selection in kernel density estimation for continuous time dependent processes," Statistics & Probability Letters, Elsevier, vol. 138(C), pages 9-19.
    3. D. Blanke & B. Pumo, 2003. "Optimal sampling for density estimation in continuous time," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(1), pages 1-23, January.
    4. Laib, Naâmane & Louani, Djamal, 2010. "Nonparametric kernel regression estimation for functional stationary ergodic data: Asymptotic properties," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2266-2281, November.
    5. Laïb, Naâmane & Louani, Djamal, 2019. "Asymptotic normality of kernel density function estimator from continuous time stationary and dependent processes," Statistics & Probability Letters, Elsevier, vol. 145(C), pages 187-196.
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    Cited by:

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