On asymptotic properties and almost sure approximation of the normalized inverse-gaussian process

Luai Al Labadi, Mahmoud Zarepour

    Research output: Contribution to journalArticlepeer-review

    10 Citations (Scopus)

    Abstract

    In this paper, similar to the frequentist asymptotic theory, we present large sample theory for the normalized inverse-Gaussian process and its corre-sponding quantile process. In particular, when the concentration parameter is large, we establish the functional central limit theorem, the strong law of large numbers and the Glivenko-Cantelli theorem for the normalized inverse-Gaussian process and its related quantile process. We also derive a finite sum representa-tion that converges almost surely to the Ferguson and Klass representation of the normalized inverse-Gaussian process. This almost sure approximation can be used to simulate the normalized inverse-Gaussian process.

    Original languageEnglish
    Pages (from-to)553-568
    Number of pages16
    JournalBayesian Analysis
    Volume8
    Issue number3
    DOIs
    Publication statusPublished - 2013

    Keywords

    • Brownian bridge
    • Dirichlet process
    • Ferguson and klass represen-tation
    • Nonparametric bayesian inference
    • Normalized inverse-gaussian process
    • Quantile process
    • Weak convergence

    ASJC Scopus subject areas

    • Statistics and Probability
    • Applied Mathematics

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