Work

Linear Wavelet-Based Estimators of Partial Derivatives of Multivariate Density Function for Stationary and Ergodic Continuous Time Processes

Year: 2025

Type: article

Abstract: In this work, we propose a wavelet-based framework for estimating the derivatives of a density function in the setting of continuous, stationary, and ergodic processes. Our primary focus is the derivation of the integrated mean square error (IMSE) over compact subsets of Rd, which provides a quantitative measure of the estimation accuracy. In addition, a uniform convergence rate and normality are established. To establish the asymptotic behavior of the proposed estimators, we adopt a martingale approach that accommodates the ergodic nature of the underlying processes. Importantly, beyond ergodicity, our analysis does not require additional assumptions regarding the data. By demonstrating that the wavelet methodology remains valid under these weaker dependence conditions, we extend earlier results originally developed in the context of independent observations.

Source: Entropy

DOI: 10.3390/e27040389

Authors: Sultana Didi, Salim Bouzebda

Institutions: Qassim University, Université de Technologie de Compiègne, Laboratoire de mathématiques appliquées de Compiègne

Language: English

Topic: Mathematical Analysis and Transform Methods

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funder: Qassim University