Perturbed datasets methods for hypothesis testing and structure of corresponding confidence sets

S. Kolumbán, I. Vajk, J.F.M. Schoukens

    Research output: Contribution to journalArticleAcademicpeer-review

    12 Citations (Scopus)

    Abstract

    Hypothesis testing methods that do not rely on exact distribution assumptions have been emerging lately. The method of sign-perturbed sums (SPS) is capable of characterizing confidence regions with exact confidence levels for linear regression and linear dynamical systems parameter estimation problems if the noise distribution is symmetric. This paper describes a general family of hypothesis testing methods that have an exact user chosen confidence level based on finite sample count and without relying on an assumed noise distribution. It is shown that the SPS method belongs to this family and we provide another hypothesis test for the case where the symmetry assumption is replaced with exchangeability. In the case of linear regression problems it is shown that the confidence regions are connected, bounded and possibly non-convex sets in both cases. To highlight the importance of understanding the structure of confidence regions corresponding to such hypothesis tests it is shown that confidence sets for linear dynamical systems parameter estimates generated using the SPS method can have non-connected parts, which have far reaching consequences.

    Original languageEnglish
    Pages (from-to)326-331
    Number of pages6
    JournalAutomatica
    Volume51
    DOIs
    Publication statusPublished - 1 Jan 2015

    Keywords

    • Confidence region
    • Finite sample
    • Guaranteed precision
    • Sign-perturbed sums

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