Robust model selection for a semimartingale continuous time regression from discrete data

Konev Victor, Pergamenchtchikov Serguei

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)

    Abstract

    The paper considers the problem of estimating a periodic function in a continuous time regression model observed under a general semimartingale noise with an unknown distribution in the case when continuous observation cannot be provided and only discrete time measurements are available. Two specific types of noises are studied in detail: a non-Gaussian Ornstein-Uhlenbeck process and a time-varying linear combination of a Brownian motion and compound Poisson process. We develop new analytical tools to treat the adaptive estimation problems from discrete data. A lower bound for the frequency sampling, needed for the efficiency of the procedure constructed by discrete observations, has been found. Sharp non-asymptotic oracle inequalities for the robust quadratic risk have been derived. New convergence rates for the efficient procedures have been obtained. An example of the regression with a martingale noise exhibits that the minimax robust convergence rate may be both higher or lower as compared with the minimax rate for the "white noise" model. The results of Monte-Carlo simulations are given.

    Original languageEnglish
    Pages (from-to)294-326
    Number of pages33
    JournalStochastic Processes and their Applications
    Volume125
    Issue number1
    DOIs
    Publication statusPublished - Jan 2015

    Keywords

    • Estimation from discrete data
    • Model selection
    • Robust risk estimation
    • Semimartingale regression
    • Sharp oracle inequalities

    ASJC Scopus subject areas

    • Modelling and Simulation
    • Statistics and Probability
    • Applied Mathematics

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