The DOI matches its Crossref record; 13 of the 13 references it cites were found in a registry or an index.
The Evaluation of General Non-Centred Orthant Probabilities
Abstract
Summary: The evaluation of the cumulative distribution function of a multivariate normal distribution is considered. The multivariate normal distribution can have any positive definite correlation matrix and any mean vector. The approach taken has two stages. In the first stage, it is shown how non-centred orthoscheme probabilities can be evaluated by using a recursive integration method. In the second stage, some ideas of Schläfli and Abrahamson are extended to show that any non-centred orthant probability can be expressed as differences between at most (m−1)! non-centred orthoscheme probabilities. This approach allows an accurate evaluation of many multivariate normal probabilities which have important applications in statistical practice.
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In the citing paper
“For example, the orthant algorithm of Miwa et al. (2003) has complexity O(d! × n), which becomes too costly for d > 10.”
From The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting (2017) · cites this paper as Miwa et al. (2003)
In the citing paper
“Even in low dimensions (d 7), the method compares favorably with highly specialized routines for orthant probabilities (Miwa et al., 2003;Craig, 2008).”
From The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting (2017) · cites this paper as Miwa et al., 2003
In the citing paper
“Unfortunately, unless a special autoregressive covariance structure is present, these methods are hardly competitive in anything but very few dimensions.”
From The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting (2017) · cites this paper as Miwa et al. (2003)
In the citing paper
“This is a rare case for which the exact value of the probability is known, namely ℓ = 1/(d + 1), and decays very slowly to zero as d ↑ ∞.”
From The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting (2017) · cites this paper as Miwa et al. (2003)
Citations
Cites
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Genz, A. (1992) · Journal of Computational and Graphical Statistics · doi:10.1080/10618600.1992.10477010 · Cited by 1,020
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Orthant Probabilities for the Quadrivariate Normal Distribution
Abrahamson, I. G. (1964) · The Annals of Mathematical Statistics · doi:10.1214/aoms/1177700391 · Cited by 60
Miwa, T., Hayter, A. J., & Liu, W. (2000) · Computational Statistics & Data Analysis · doi:10.1016/s0167-9473(99)00075-4 · Cited by 21
Self-citation
Research works printed but not linked: 2
- Hayter, 1996, A note on the calculation of & pr ;{X1 < X2 < ⋯ < Xk}, Am. Statistn, 50, 365
- Schläfli, 1858, On the multiple integral ∫ndxdy…dz, whose limits are p1=a1x+b1y+…+h1z > 0,p2 > 0,…,pn > 0, and x2+y2+…+z2 < 1, Q. J. Pure Appl. Math., 2, 269
Cited by
The Normal Law Under Linear Restrictions: Simulation and Estimation via Minimax Tilting
Botev, Z. I. (2017) · Journal of the Royal Statistical Society Series B: Statistical Methodology · doi:10.1111/rssb.12162 · Cited by 247
Gaussian copula marginal regression
Masarotto, G., & Varin, C. (2012) · Electronic Journal of Statistics · doi:10.1214/12-ejs721 · Cited by 182
Models for Paired Comparison Data: A Review with Emphasis on Dependent Data
Cattelan, M. (2012) · Statistical Science · doi:10.1214/12-sts396 · Cited by 167
mvtnorm: Multivariate Normal and t Distributions
Genz, A., Bretz, F., Miwa, T., Mi, X., & Hothorn, T. (2000) · CRAN: Contributed Packages · doi:10.32614/cran.package.mvtnorm · Cited by 162
Self-citationStochastic Linear Hybrid Systems: Modeling, Estimation, and Application in Air Traffic Control
Seah, C. E., & Hwang, I. (2009) · IEEE Transactions on Control Systems Technology · doi:10.1109/tcst.2008.2001377 · Cited by 85
Metadata
- Authors
- Miwa, T., Hayter, A. J., & Kuriki, S.
- Affiliations
- National Institute for Agro-Environmental Sciences (JP)
- Georgia Institute of Technology (US)
- The Institute of Statistical Mathematics (JP)
- Corresponding author
- Miwa, Tetsuhisa
- ORCID
- Kuriki, Satoshi
- Venue
- Journal of the Royal Statistical Society Series B: Statistical Methodology
- Publisher
- Oxford University Press (OUP)
- Published
- 2003-01-28
- Volume
- 65
- Issue
- 1
- Pages
- 223-234
- ISSN
- 1369-7412 (ISSN-L)
- 1467-9868
- OpenAlex
- W2150991310
- Cited by
- 100
- References
- 13
- Citations by year
- 2026: 5 · 2025: 6 · 2024: 2 · 2023: 8 · 2022: 3 · 2021: 7 · 2020: 6 · 2019: 6 · 2018: 2 · 2017: 7 · 2016: 5 · 2015: 11 · 2014: 6 · 2013: 2 · 2012: 6
- FWCI
- 0.94
- Type
- journal article
- Language
- en
- Open access
- closed
- Licence
- academic.oup.com/journals/pages/open_access/funder_policies/chorus/standard_publication_model (vor)
- Locations
- Journal of the Royal Statistical Society Series B (Statistical Methodology) (publishedVersion)
- RePEc: Research Papers in Economics (submittedVersion)
- Topics
- Physical Sciences › Mathematics › Statistics and Probability › Statistical Distribution Estimation and Applications
- Physical Sciences › Mathematics › Statistics and Probability › Probability and Statistical Research
- Physical Sciences › Mathematics › Applied Mathematics › Mathematical functions and polynomials
- Keywords
- multivariate normal distribution, cumulative distribution function, recursive integration, correlation matrix, mean vector
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- Miwa, T., Hayter, A. J., & Kuriki, S. (2003). The Evaluation of General Non-Centred Orthant Probabilities. Journal of the Royal Statistical Society Series B: Statistical Methodology. https://doi.org/10.1111/1467-9868.00382
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Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
