Published December 2022
| Submitted + Supplemental Material
Journal Article
Open
A multivariate normal approximation for the Dirichlet density and some applications
- Creators
- Ouimet, Frédéric
Abstract
In this short note, we prove an asymptotic expansion for the ratio of the Dirichlet density to the multivariate normal density with the same mean and covariance matrix. The expansion is then used to derive an upper bound on the total variation between the corresponding probability measures and rederive the asymptotic variance of the Dirichlet kernel estimators introduced by Aitchison and Lauder (1985) and studied theoretically in Ouimet (2020). Another potential application related to the asymptotic equivalence between the Gaussian variance regression problem and the Gaussian white noise problem is briefly mentioned but left open for future research.
Additional Information
© 2021 Wiley. Issue Online: 01 March 2022; Version of Record online: 01 March 2022; Accepted manuscript online: 24 August 2021; Manuscript accepted: 10 August 2021; Manuscript revised: 28 July 2021; Manuscript received: 22 June 2021. The author acknowledges support of a postdoctoral fellowship from the NSERC (PDF) and the FRQNT (B3X supplement). We thank the referees for their valuable comments that led to improvements in the presentation of this paper. Data Availability Statement: The R code that generated all the figures in Appendix B is available as supplemental material online.Attached Files
Submitted - 2103.02853.pdf
Supplemental Material - sta4410-sup-0001-simulations.r
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2103.02853.pdf
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Additional details
- Alternative title
- Upper bound on the total variation between Dirichlet and multivariate normal distributions
- Eprint ID
- 110688
- Resolver ID
- CaltechAUTHORS:20210901-153909471
- Natural Sciences and Engineering Research Council of Canada (NSERC)
- B3X
- Fonds de recherche du Québec - Nature et technologies (FRQNT)
- Created
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2021-09-01Created from EPrint's datestamp field
- Updated
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2022-03-14Created from EPrint's last_modified field