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Minimax estimation of the diffusion coefficient through irregular samplings

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  • Hoffmann, Marc

Abstract

We study the problem of estimating the time dependent diffusion coefficient of a diffusion process in a nonparametric setting, when the sample path is observed at discrete times. We look at global Lp-error loss over a wide range of function spaces (namely, Besov spaces). We exhibit the minimax rate of convergence over linear estimators and provide estimators based on fast wavelets methods which are optimal. Our method takes into account functional estimation on the interval (with edges effects) and allows to consider irregular sampling schemes.

Suggested Citation

  • Hoffmann, Marc, 1997. "Minimax estimation of the diffusion coefficient through irregular samplings," Statistics & Probability Letters, Elsevier, vol. 32(1), pages 11-24, February.
    • Handle: RePEc:eee:stapro:v:32:y:1997:i:1:p:11-24
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    References listed on IDEAS

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    1. Jacod, J., 1993. "Random sampling in estimation problems for continuous Gaussian processes with independent increments," Stochastic Processes and their Applications, Elsevier, vol. 44(2), pages 181-204, February.
    2. Kerkyacharian, G. & Picard, D., 1992. "Density estimation in Besov spaces," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 15-24, January.
    3. Kerkyacharian, Gérard & Picard, Dominique, 1993. "Density estimation by kernel and wavelets methods: Optimality of Besov spaces," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 327-336, November.
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    1. Olivier Féron & Pierre Gruet & Marc Hoffmann, 2020. "Efficient volatility estimation in a two‐factor model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 862-898, September.

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