Bounds in Wasserstein distance for locally stationary processes

• URL: http://arxiv.org/abs/2412.03414v1
• Date: Wed, 04 Dec 2024 15:51:22 GMT
• Title: Bounds in Wasserstein distance for locally stationary processes
• Authors: Jan Nino G. Tinio, Mokhtar Z. Alaya, Salim Bouzebda,
• Abstract summary: We address the estimation of the conditional probability distribution of locally stationary processes (LSPs) using Nadaraya-Watson type estimators. Results are supported by numerical experiments on both synthetic and real-world datasets.
• Score: 2.180952057802427
• License:
• Abstract: Locally stationary processes (LSPs) provide a robust framework for modeling time-varying phenomena, allowing for smooth variations in statistical properties such as mean and variance over time. In this paper, we address the estimation of the conditional probability distribution of LSPs using Nadaraya-Watson (NW) type estimators. The NW estimator approximates the conditional distribution of a target variable given covariates through kernel smoothing techniques. We establish the convergence rate of the NW conditional probability estimator for LSPs in the univariate setting under the Wasserstein distance and extend this analysis to the multivariate case using the sliced Wasserstein distance. Theoretical results are supported by numerical experiments on both synthetic and real-world datasets, demonstrating the practical usefulness of the proposed estimators.

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