Adaptive wavelet estimation of a function from an m-dependent process with possibly unbounded m

Christophe Chesneau*, Hassan Doosti, Lewi Stone

*Corresponding author for this work

    Research output: Contribution to journalArticlepeer-review

    2 Citations (Scopus)

    Abstract

    The estimation of a multivariate function from a stationary m-dependent process is investigated, with a special focus on the case where m is large or unbounded. We develop an adaptive estimator based on wavelet methods. Under flexible assumptions on the nonparametric model, we prove the good performances of our estimator by determining sharp rates of convergence under two kinds of errors: the pointwise mean squared error and the mean integrated squared error. We illustrate our theoretical result by considering the multivariate density estimation problem, the derivatives density estimation problem, the density estimation problem in a GARCH-type model and the multivariate regression function estimation problem. The performance of proposed estimator has been shown by a numerical study for a simulated and real data sets.

    Original languageEnglish
    Pages (from-to)1123-1135
    Number of pages13
    JournalCommunications in Statistics - Theory and Methods
    Volume48
    Issue number5
    Early online date2018
    DOIs
    Publication statusPublished - 2019

    Keywords

    • Density estimation
    • m-dependence
    • Nonparametric regression
    • Rates of convergence
    • Wavelet methods.

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