Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic Processes
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 <inline-formula><math xmlns="...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-05-01
|
| Series: | Mathematics |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2227-7390/13/10/1587 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1850257589486485504 |
|---|---|
| author | Sultana Didi Salim Bouzebda |
| author_facet | Sultana Didi Salim Bouzebda |
| author_sort | Sultana Didi |
| collection | DOAJ |
| description | 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></semantics></math></inline-formula>, 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. |
| format | Article |
| id | doaj-art-463efc8db7c7417185dc9dcc6c634020 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-463efc8db7c7417185dc9dcc6c6340202025-08-20T01:56:24ZengMDPI AGMathematics2227-73902025-05-011310158710.3390/math13101587Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic ProcessesSultana Didi0Salim Bouzebda1Department of Statistics and Operations Research, College of Sciences, Qassim University, P.O. Box 6688, Buraydah 51452, Saudi ArabiaUniversité de Technologie de Compiègne, LMAC (Laboratory of Applied Mathematics of Compiègne), CS 60 319-60 203 Compiègne, FranceThis 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 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi mathvariant="double-struck">R</mi><mi>d</mi></msup></semantics></math></inline-formula>, 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.https://www.mdpi.com/2227-7390/13/10/1587regression estimationstationarityergodicityrates of strong convergencewavelet-based estimatorsmartingale differences |
| spellingShingle | Sultana Didi Salim Bouzebda Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic Processes Mathematics regression estimation stationarity ergodicity rates of strong convergence wavelet-based estimators martingale differences |
| title | Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic Processes |
| title_full | Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic Processes |
| title_fullStr | Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic Processes |
| title_full_unstemmed | Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic Processes |
| title_short | Wavelet Estimation of Partial Derivatives in Multivariate Regression Under Discrete-Time Stationary Ergodic Processes |
| title_sort | wavelet estimation of partial derivatives in multivariate regression under discrete time stationary ergodic processes |
| topic | regression estimation stationarity ergodicity rates of strong convergence wavelet-based estimators martingale differences |
| url | https://www.mdpi.com/2227-7390/13/10/1587 |
| work_keys_str_mv | AT sultanadidi waveletestimationofpartialderivativesinmultivariateregressionunderdiscretetimestationaryergodicprocesses AT salimbouzebda waveletestimationofpartialderivativesinmultivariateregressionunderdiscretetimestationaryergodicprocesses |