Moment convergence in regularized estimation under multiple and mixed-rates asymptotics

H. Masuda, Y. Shimizu

    Research output: Contribution to journalArticlepeer-review

    12 Citations (Scopus)


    In M-estimation under standard asymptotics, the weak convergence combined with the polynomial type large deviation estimate of the associated statistical random field Yoshida (2011) provides us with not only the asymptotic distribution of the associated M-estimator but also the convergence of its moments, the latter playing an important role in theoretical statistics. In this paper, we study the above program for statistical random fields of multiple and also possibly mixedrates type in the sense of Radchenko (2008) where the associated statistical random fields may be nondifferentiable and may fail to be locally asymptotically quadratic. Consequently, a very strong mode of convergence of a wide range of regularized M-estimators is ensured.Our results are applied to regularized estimation of an ergodic diffusion observed at high frequency.

    Original languageEnglish
    Pages (from-to)81-110
    Number of pages30
    JournalMathematical Methods of Statistics
    Issue number2
    Publication statusPublished - Apr 1 2017

    All Science Journal Classification (ASJC) codes

    • Statistics and Probability
    • Statistics, Probability and Uncertainty


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