IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v10y2022i19p3433-d921038.html
   My bibliography  Save this article

Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time

Author

Listed:
  • Sultana DIDI

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

  • Ahoud AL HARBY

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

  • Salim BOUZEBDA

    (LMAC (Laboratory of Applied Mathematics of Compiègne), Université de Technologie de Compiègne, 60200 Compiègne, France
    These authors contributed equally to this work.)

Abstract

The nonparametric estimation of density and regression function based on functional stationary processes using wavelet bases for Hilbert spaces of functions is investigated in this paper. The mean integrated square error over adapted decomposition spaces is given. To obtain the asymptotic properties of wavelet density and regression estimators, the Martingale method is used. These results are obtained under some mild conditions on the model; aside from ergodicity, no other assumptions are imposed on the data. This paper extends the scope of some previous results for wavelet density and regression estimators by relaxing the independence or the mixing condition to the ergodicity. Potential applications include the conditional distribution, curve discrimination, and time series prediction from a continuous set of past values.

Suggested Citation

  • Sultana DIDI & Ahoud AL HARBY & Salim BOUZEBDA, 2022. "Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time," Mathematics, MDPI, vol. 10(19), pages 1-33, September.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3433-:d:921038
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/10/19/3433/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/10/19/3433/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Ibrahim M. Almanjahie & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Estimating the Conditional Density in Scalar-On-Function Regression Structure: k -N-N Local Linear Approach," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    2. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    3. Ibrahim M. Almanjahie & Salim Bouzebda & Zoulikha Kaid & Ali Laksaci, 2022. "Nonparametric estimation of expectile regression in functional dependent data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 34(1), pages 250-281, January.
    4. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.
    5. Salim Bouzebda & Boutheina Nemouchi, 2020. "Uniform consistency and uniform in bandwidth consistency for nonparametric regression estimates and conditional U-statistics involving functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 32(2), pages 452-509, April.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sultana Didi & Salim Bouzebda, 2022. "Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes," Mathematics, MDPI, vol. 10(22), pages 1-37, November.
    2. Salim Bouzebda & Inass Soukarieh, 2022. "Non-Parametric Conditional U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 11(1), pages 1-69, December.
    3. Fatimah A. Almulhim & Mohammed B. Alamari & Salim Bouzebda & Zoulikha Kaid & Ali Laksaci, 2025. "Robust Estimation of L 1 -Modal Regression Under Functional Single-Index Models for Practical Applications," Mathematics, MDPI, vol. 13(4), pages 1-20, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Sultana Didi & Salim Bouzebda, 2022. "Wavelet Density and Regression Estimators for Continuous Time Functional Stationary and Ergodic Processes," Mathematics, MDPI, vol. 10(22), pages 1-37, November.
    2. Bouzebda, Salim & Chaouch, Mohamed, 2022. "Uniform limit theorems for a class of conditional Z-estimators when covariates are functions," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    3. Salim Bouzebda & Boutheina Nemouchi, 2023. "Weak-convergence of empirical conditional processes and conditional U-processes involving functional mixing data," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 33-88, April.
    4. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    5. Klaus Ackermann & Simon D Angus & Paul A Raschky, 2020. "Estimating Sleep and Work Hours from Alternative Data by Segmented Functional Classification Analysis, SFCA," SoDa Laboratories Working Paper Series 2020-04, Monash University, SoDa Laboratories.
    6. Soukarieh, Inass & Bouzebda, Salim, 2023. "Renewal type bootstrap for increasing degree U-process of a Markov chain," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    7. Salim Bouzebda & Yousri Slaoui, 2023. "Nonparametric Recursive Estimation for Multivariate Derivative Functions by Stochastic Approximation Method," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 658-690, February.
    8. Shang, Han Lin & Kearney, Fearghal, 2022. "Dynamic functional time-series forecasts of foreign exchange implied volatility surfaces," International Journal of Forecasting, Elsevier, vol. 38(3), pages 1025-1049.
    9. Fabrizio Maturo & Antonio Balzanella & Tonio Di Battista, 2019. "Building Statistical Indicators of Equitable and Sustainable Well-Being in a Functional Framework," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 146(3), pages 449-471, December.
    10. Salim Bouzebda & Thouria El-hadjali & Anouar Abdeldjaoued Ferfache, 2023. "Uniform in Bandwidth Consistency of Conditional U-statistics Adaptive to Intrinsic Dimension in Presence of Censored Data," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1548-1606, August.
    11. Klaus Ackermann & Simon D. Angus & Paul A. Raschky, 2020. "Estimating Sleep & Work Hours from Alternative Data by Segmented Functional Classification Analysis (SFCA)," Papers 2010.08102, arXiv.org.
    12. Litimein, Ouahiba & Laksaci, Ali & Ait-Hennani, Larbi & Mechab, Boubaker & Rachdi, Mustapha, 2024. "Asymptotic normality of the local linear estimator of the functional expectile regression," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    13. Joseph Y. Nashed & Daniel J. Gale & Jason P. Gallivan & Douglas J. Cook, 2024. "Changes in cortical manifold structure following stroke and its relation to behavioral recovery in the male macaque," Nature Communications, Nature, vol. 15(1), pages 1-17, December.
    14. Bodnar, Taras & Okhrin, Ostap & Parolya, Nestor, 2019. "Optimal shrinkage estimator for high-dimensional mean vector," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 63-79.
    15. Hron, K. & Menafoglio, A. & Templ, M. & Hrůzová, K. & Filzmoser, P., 2016. "Simplicial principal component analysis for density functions in Bayes spaces," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 330-350.
    16. Reid, Nancy, 2018. "Statistical science in the world of big data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 42-45.
    17. Groll, Andreas & López-Cabrera, Brenda & Meyer-Brandis, Thilo, 2016. "A consistent two-factor model for pricing temperature derivatives," Energy Economics, Elsevier, vol. 55(C), pages 112-126.
    18. Bouzebda, Salim & Slaoui, Yousri, 2022. "Nonparametric recursive method for moment generating function kernel-type estimators," Statistics & Probability Letters, Elsevier, vol. 184(C).
    19. Steven Campbell & Ting-Kam Leonard Wong, 2022. "Efficient convex PCA with applications to Wasserstein GPCA and ranked data," Papers 2211.02990, arXiv.org, revised Aug 2024.
    20. Justin Petrovich & Matthew Reimherr & Carrie Daymont, 2022. "Highly irregular functional generalized linear regression with electronic health records," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(4), pages 806-833, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:10:y:2022:i:19:p:3433-:d:921038. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.