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

Author

Listed:
  • Sultana Didi

    (Department of Statistics and Operations Research, College of Sciences, Qassim University, P.O. Box 6688, Buraydah 51452, Saudi Arabia
    These authors contributed equally to this work.)

  • Salim Bouzebda

    (Université de Technologie de Compiègne, LMAC (Laboratory of Applied Mathematics of Compiègne), CS 60 319-60 203 Compiègne, France
    These authors contributed equally to this work.)

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.

Suggested Citation

  • Sultana Didi & Salim Bouzebda, 2025. "Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic Processes," Mathematics, MDPI, vol. 13(10), pages 1-36, May.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:10:p:1587-:d:1654016
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    References listed on IDEAS

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