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Nonparametric Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion with Random Effects

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  • B. L. S. Prakasa Rao

    (CR RAO Advanced Institute of Mathematics, Statistics and Computer Science)

Abstract

We discuss nonparametric estimation of the density of random effects in models governed by a stochastic differential equation driven by a mixed fractional Brownian motion.

Suggested Citation

  • B. L. S. Prakasa Rao, 2021. "Nonparametric Estimation for Stochastic Differential Equations Driven by Mixed Fractional Brownian Motion with Random Effects," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 554-568, August.
    • Handle: RePEc:spr:sankha:v:83:y:2021:i:2:d:10.1007_s13171-020-00230-3
    DOI: 10.1007/s13171-020-00230-3
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    References listed on IDEAS

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    1. Picchini, Umberto & Ditlevsen, Susanne, 2011. "Practical estimation of high dimensional stochastic differential mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1426-1444, March.
    2. Hu, Yaozhong & Nualart, David & Song, Xiaoming, 2008. "A singular stochastic differential equation driven by fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2075-2085, October.
    3. L. Nie, 2006. "Strong Consistency of the Maximum Likelihood Estimator in Generalized Linear and Nonlinear Mixed-Effects Models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 63(2), pages 123-143, April.
    4. Antic, J. & Laffont, C.M. & Chafaï, D. & Concordet, D., 2009. "Comparison of nonparametric methods in nonlinear mixed effects models," Computational Statistics & Data Analysis, Elsevier, vol. 53(3), pages 642-656, January.
    5. Mémin, Jean & Mishura, Yulia & Valkeila, Esko, 2001. "Inequalities for the moments of Wiener integrals with respect to a fractional Brownian motion," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 197-206, January.
    6. Umberto Picchini & Andrea De Gaetano & Susanne Ditlevsen, 2010. "Stochastic Differential Mixed‐Effects Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(1), pages 67-90, March.
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