Multivariate normal distribution (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Multivariate normal distribution" in English language version.

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19doi.org

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arxiv.org

Botev, Z. I. (2016). "The normal law under linear restrictions: simulation and estimation via minimax tilting". Journal of the Royal Statistical Society, Series B. 79: 125–148. arXiv:1603.04166. Bibcode:2016arXiv160304166B. doi:10.1111/rssb.12162. S2CID 88515228.
Das, Abhranil; Wilson S Geisler (2020). "Methods to integrate multinormals and compute classification measures". arXiv:2012.14331 [stat.ML].
Nikolaus Hansen (2016). "The CMA Evolution Strategy: A Tutorial" (PDF). arXiv:1604.00772. Bibcode:2016arXiv160400772H. Archived from the original (PDF) on 2010-03-31. Retrieved 2012-01-07.

cern.ch

cds.cern.ch

Gentle, J. E. (2009). Computational Statistics. Statistics and Computing. New York: Springer. pp. 315–316. doi:10.1007/978-0-387-98144-4. ISBN 978-0-387-98143-7.

colorado.edu

amath.colorado.edu

Tong, T. (2010) Multiple Linear Regression : MLE and Its Distributional Results Archived 2013-06-16 at WebCite, Lecture Notes

computervisionmodels.com

Simon J.D. Prince(June 2012). Computer Vision: Models, Learning, and Inference Archived 2020-10-28 at the Wayback Machine. Cambridge University Press. 3.7:"Multivariate normal distribution".

doi.org

Kac, M. (1939). "On a characterization of the normal distribution". American Journal of Mathematics. 61 (3): 726–728. doi:10.2307/2371328. JSTOR 2371328.
Sinz, Fabian; Gerwinn, Sebastian; Bethge, Matthias (2009). "Characterization of the p-generalized normal distribution". Journal of Multivariate Analysis. 100 (5): 817–820. doi:10.1016/j.jmva.2008.07.006.
Kim, M. G. (2000). "Multivariate outliers and decompositions of Mahalanobis distance". Communications in Statistics – Theory and Methods. 29 (7): 1511–1526. doi:10.1080/03610920008832559.
Hamedani, G. G.; Tata, M. N. (1975). "On the determination of the bivariate normal distribution from distributions of linear combinations of the variables". The American Mathematical Monthly. 82 (9): 913–915. doi:10.2307/2318494. JSTOR 2318494.
Botev, Z. I. (2016). "The normal law under linear restrictions: simulation and estimation via minimax tilting". Journal of the Royal Statistical Society, Series B. 79: 125–148. arXiv:1603.04166. Bibcode:2016arXiv160304166B. doi:10.1111/rssb.12162. S2CID 88515228.
Siotani, Minoru (1964). "Tolerance regions for a multivariate normal population" (PDF). Annals of the Institute of Statistical Mathematics. 16 (1): 135–153. doi:10.1007/BF02868568. S2CID 123269490.
Botev, Z. I.; Mandjes, M.; Ridder, A. (6–9 December 2015). "Tail distribution of the maximum of correlated Gaussian random variables". 2015 Winter Simulation Conference (WSC). Huntington Beach, Calif., USA: IEEE. pp. 633–642. doi:10.1109/WSC.2015.7408202. hdl:10419/130486. ISBN 978-1-4673-9743-8.
Adler, R. J.; Blanchet, J.; Liu, J. (7–10 Dec 2008). "Efficient simulation for tail probabilities of Gaussian random fields". 2008 Winter Simulation Conference (WSC). Miami, Fla., USA: IEEE. pp. 328–336. doi:10.1109/WSC.2008.4736085. ISBN 978-1-4244-2707-9.
Hernandez-Stumpfhauser, Daniel; Breidt, F. Jay; van der Woerd, Mark J. (2017). "The General Projected Normal Distribution of Arbitrary Dimension: Modeling and Bayesian Inference". Bayesian Analysis. 12 (1): 113–133. doi:10.1214/15-BA989.
Gokhale, DV; Ahmed, NA; Res, BC; Piscataway, NJ (May 1989). "Entropy Expressions and Their Estimators for Multivariate Distributions". IEEE Transactions on Information Theory. 35 (3): 688–692. doi:10.1109/18.30996.
Wang, Bin; Shi, Wenzhong; Miao, Zelang (2015-03-13). Rocchini, Duccio (ed.). "Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space". PLOS ONE. 10 (3): e0118537. Bibcode:2015PLoSO..1018537W. doi:10.1371/journal.pone.0118537. ISSN 1932-6203. PMC 4358977. PMID 25769048.
Cox, D. R.; Small, N. J. H. (1978). "Testing multivariate normality". Biometrika. 65 (2): 263. doi:10.1093/biomet/65.2.263.
Smith, S. P.; Jain, A. K. (1988). "A test to determine the multivariate normality of a data set". IEEE Transactions on Pattern Analysis and Machine Intelligence. 10 (5): 757. doi:10.1109/34.6789.
Friedman, J. H.; Rafsky, L. C. (1979). "Multivariate Generalizations of the Wald–Wolfowitz and Smirnov Two-Sample Tests". The Annals of Statistics. 7 (4): 697. doi:10.1214/aos/1176344722.
Mardia, K. V. (1970). "Measures of multivariate skewness and kurtosis with applications". Biometrika. 57 (3): 519–530. doi:10.1093/biomet/57.3.519.
Baringhaus, L.; Henze, N. (1991). "Limit distributions for measures of multivariate skewness and kurtosis based on projections". Journal of Multivariate Analysis. 38: 51–69. doi:10.1016/0047-259X(91)90031-V.
Baringhaus, L.; Henze, N. (1988). "A consistent test for multivariate normality based on the empirical characteristic function". Metrika. 35 (1): 339–348. doi:10.1007/BF02613322. S2CID 122362448.
Henze, Norbert (2002). "Invariant tests for multivariate normality: a critical review". Statistical Papers. 43 (4): 467–506. doi:10.1007/s00362-002-0119-6. S2CID 122934510.
Gentle, J. E. (2009). Computational Statistics. Statistics and Computing. New York: Springer. pp. 315–316. doi:10.1007/978-0-387-98144-4. ISBN 978-0-387-98143-7.

handle.net

hdl.handle.net

Botev, Z. I.; Mandjes, M.; Ridder, A. (6–9 December 2015). "Tail distribution of the maximum of correlated Gaussian random variables". 2015 Winter Simulation Conference (WSC). Huntington Beach, Calif., USA: IEEE. pp. 633–642. doi:10.1109/WSC.2015.7408202. hdl:10419/130486. ISBN 978-1-4673-9743-8.

harvard.edu

ui.adsabs.harvard.edu

Botev, Z. I. (2016). "The normal law under linear restrictions: simulation and estimation via minimax tilting". Journal of the Royal Statistical Society, Series B. 79: 125–148. arXiv:1603.04166. Bibcode:2016arXiv160304166B. doi:10.1111/rssb.12162. S2CID 88515228.
Nikolaus Hansen (2016). "The CMA Evolution Strategy: A Tutorial" (PDF). arXiv:1604.00772. Bibcode:2016arXiv160400772H. Archived from the original (PDF) on 2010-03-31. Retrieved 2012-01-07.
Wang, Bin; Shi, Wenzhong; Miao, Zelang (2015-03-13). Rocchini, Duccio (ed.). "Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space". PLOS ONE. 10 (3): e0118537. Bibcode:2015PLoSO..1018537W. doi:10.1371/journal.pone.0118537. ISSN 1932-6203. PMC 4358977. PMID 25769048.

hmc.edu

fourier.eng.hmc.edu

An algebraic computation of the marginal distribution is shown here http://fourier.eng.hmc.edu/e161/lectures/gaussianprocess/node7.html Archived 2010-01-17 at the Wayback Machine. A much shorter proof is outlined here https://math.stackexchange.com/a/3832137

ism.ac.jp

Siotani, Minoru (1964). "Tolerance regions for a multivariate normal population" (PDF). Annals of the Institute of Statistical Mathematics. 16 (1): 135–153. doi:10.1007/BF02868568. S2CID 123269490.

jstor.org

Kac, M. (1939). "On a characterization of the normal distribution". American Journal of Mathematics. 61 (3): 726–728. doi:10.2307/2371328. JSTOR 2371328.
Hamedani, G. G.; Tata, M. N. (1975). "On the determination of the bivariate normal distribution from distributions of linear combinations of the variables". The American Mathematical Monthly. 82 (9): 913–915. doi:10.2307/2318494. JSTOR 2318494.

lri.fr

Nikolaus Hansen (2016). "The CMA Evolution Strategy: A Tutorial" (PDF). arXiv:1604.00772. Bibcode:2016arXiv160400772H. Archived from the original (PDF) on 2010-03-31. Retrieved 2012-01-07.

mit.edu

web.mit.edu

Wyatt, John (November 26, 2008). "Linear least mean-squared error estimation" (PDF). Lecture notes course on applied probability. Archived from the original (PDF) on October 10, 2015. Retrieved 23 January 2012.

nih.gov

ncbi.nlm.nih.gov

Wang, Bin; Shi, Wenzhong; Miao, Zelang (2015-03-13). Rocchini, Duccio (ed.). "Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space". PLOS ONE. 10 (3): e0118537. Bibcode:2015PLoSO..1018537W. doi:10.1371/journal.pone.0118537. ISSN 1932-6203. PMC 4358977. PMID 25769048.

pubmed.ncbi.nlm.nih.gov

Wang, Bin; Shi, Wenzhong; Miao, Zelang (2015-03-13). Rocchini, Duccio (ed.). "Confidence Analysis of Standard Deviational Ellipse and Its Extension into Higher Dimensional Euclidean Space". PLOS ONE. 10 (3): e0118537. Bibcode:2015PLoSO..1018537W. doi:10.1371/journal.pone.0118537. ISSN 1932-6203. PMC 4358977. PMID 25769048.

semanticscholar.org

api.semanticscholar.org

Botev, Z. I. (2016). "The normal law under linear restrictions: simulation and estimation via minimax tilting". Journal of the Royal Statistical Society, Series B. 79: 125–148. arXiv:1603.04166. Bibcode:2016arXiv160304166B. doi:10.1111/rssb.12162. S2CID 88515228.
Siotani, Minoru (1964). "Tolerance regions for a multivariate normal population" (PDF). Annals of the Institute of Statistical Mathematics. 16 (1): 135–153. doi:10.1007/BF02868568. S2CID 123269490.
Baringhaus, L.; Henze, N. (1988). "A consistent test for multivariate normality based on the empirical characteristic function". Metrika. 35 (1): 339–348. doi:10.1007/BF02613322. S2CID 122362448.
Henze, Norbert (2002). "Invariant tests for multivariate normality: a critical review". Statistical Papers. 43 (4): 467–506. doi:10.1007/s00362-002-0119-6. S2CID 122934510.