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Evolving privacy: Drift parameter estimation for discretely observed i.i.d. diffusion processes under LDP

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  • Amorino, Chiara
  • Gloter, Arnaud
  • Halconruy, Hélène

Abstract

The problem of estimating a parameter in the drift coefficient is addressed for N discretely observed independent and identically distributed stochastic differential equations (SDEs). This is done considering additional constraints, wherein only public data can be published and used for inference. The concept of local differential privacy (LDP) is formally introduced for a system of stochastic differential equations. The objective is to estimate the drift parameter by proposing a contrast function based on a pseudo-likelihood approach. A suitably scaled Laplace noise is incorporated to meet the privacy requirements. Our key findings encompass the derivation of explicit conditions tied to the privacy level. Under these conditions, we establish the consistency and asymptotic normality of the associated estimator. Notably, the convergence rate is intricately linked to the privacy level, and in some situations may be completely different from the case where privacy constraints are ignored. Our results hold true as the discretization step approaches zero and the number of processes N tends to infinity.

Suggested Citation

  • Amorino, Chiara & Gloter, Arnaud & Halconruy, Hélène, 2025. "Evolving privacy: Drift parameter estimation for discretely observed i.i.d. diffusion processes under LDP," Stochastic Processes and their Applications, Elsevier, vol. 181(C).
  • Handle: RePEc:eee:spapps:v:181:y:2025:i:c:s0304414924002655
    DOI: 10.1016/j.spa.2024.104557
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    References listed on IDEAS

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    1. Chiara Amorino & Arnaud Gloter, 2020. "Contrast function estimation for the drift parameter of ergodic jump diffusion process," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 279-346, June.
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    6. Amorino, Chiara & Heidari, Akram & Pilipauskaitė, Vytautė & Podolskij, Mark, 2023. "Parameter estimation of discretely observed interacting particle systems," Stochastic Processes and their Applications, Elsevier, vol. 163(C), pages 350-386.
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