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 language | English |
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Pages (from-to) | 553-568 |
Number of pages | 16 |
Journal | Bayesian Analysis |
Volume | 8 |
Issue number | 3 |
DOIs | |
Publication status | Published - 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