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Statistical Skorohod embedding problem: Optimality and asymptotic normality

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  • Belomestny, Denis
  • Schoenmakers, John

Abstract

Given a Brownian motion B, we consider the so-called statistical Skorohod embedding problem of recovering the distribution of an independent random time T based on i.i.d. sample from BT. We propose a consistent estimator for the density of T, derive its convergence rates and prove their optimality.

Suggested Citation

  • Belomestny, Denis & Schoenmakers, John, 2015. "Statistical Skorohod embedding problem: Optimality and asymptotic normality," Statistics & Probability Letters, Elsevier, vol. 104(C), pages 169-180.
    • Handle: RePEc:eee:stapro:v:104:y:2015:i:c:p:169-180
    DOI: 10.1016/j.spl.2015.05.015
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    References listed on IDEAS

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    1. Van Es, Bert & Spreij, Peter, 2011. "Estimation of a multivariate stochastic volatility density by kernel deconvolution," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 683-697, March.
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    Cited by:

    1. Belomestny, Denis & Schoenmakers, John, 2016. "Statistical inference for time-changed Lévy processes via Mellin transform approach," Stochastic Processes and their Applications, Elsevier, vol. 126(7), pages 2092-2122.
    2. Viktor Schulmann, 2021. "Estimation of stopping times for stopped self-similar random processes," Statistical Inference for Stochastic Processes, Springer, vol. 24(2), pages 477-498, July.

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