Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic Processes

Sultana Didi and Salim Bouzebda ()
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Sultana Didi: Department of Statistics and Operations Research, College of Sciences, Qassim University, P.O. Box 6688, Buraydah 51452, Saudi Arabia
Salim Bouzebda: Université de technologie de Compiègne, LMAC (Laboratory of Applied Mathematics of Compiègne), CS 60 319-60 203 Compiègne, France

Mathematics, 2025, vol. 13, issue 10, 1-36

Abstract: This study introduces a wavelet-based framework for estimating derivatives of a general regression function within discrete-time, stationary ergodic processes. The analysis focuses on deriving the integrated mean squared error (IMSE) over compact subsets of R d , while also establishing rates of uniform convergence and the asymptotic normality of the proposed estimators. To investigate their asymptotic behavior, we adopt a martingale-based approach specifically adapted to the ergodic nature of the data-generating process. Importantly, the framework imposes no structural assumptions beyond ergodicity, thereby circumventing restrictive dependence conditions. By establishing the limiting behavior of the wavelet estimators under these minimal assumptions, the results extend existing findings for independent data and highlight the flexibility of wavelet methods in more general stochastic settings.

Keywords: regression estimation; stationarity; ergodicity; rates of strong convergence; wavelet-based estimators; martingale differences; discrete time; stochastic processes; time series (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:10:p:1587-:d:1654016

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