Ousmane Sacko | Searcharxiv

arXiv2025

Nadaraya-Watson Type Estimator of the Transition Density Function for Diffusion Processes

This paper deals with a nonparametric Nadaraya-Watson (NW) estimator of the transition density function computed from independent continuous observations of a diffusion process. A risk bound is established on this estimator. The paper also deals with an extension of the penalized comparison to overfitting bandwidths selection method for our NW estimator. Finally, numerical experiments are provided.

math.ST↗

arXiv2024

Minimax density estimation in the adversarial framework under local differential privacy

We consider the problem of nonparametric density estimation under privacy constraints in an adversarial framework. To this end, we study minimax rates over Sobolev spaces under local differential privacy. We first obtain a lower bound which allows us to quantify the impact of privacy compared with the classical framework. Next, we introduce a new Coordinate block privacy mechanism that guarantees local differential privacy, which, coupled with a projection estimator, achieves the minimax optimal rates. Finally, we develop an adaptive procedure which is optimal in the minimax sense up to logarithmic terms.

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