RafterNet: Probabilistic Predictions in Multi-Response Regression

References

• Barriga, G. D. C., Louzada-Neto, F., Ortega, E. M. M., and Cancho, V. G. (2010), “A Bivariate Regression Model for Matched Paired Survival Data: Local Influence and Residual Analysis,” Statistical Methods & Applications, 19, 477–495.
   Web of Science ®Google Scholar
• Breiman, L. (2001), “Random Forests,” Machine Learning, 45, 5–32. DOI: 10.1023/A:1010933404324.
   Web of Science ®Google Scholar
• Côté, M.-P., Genest, C., and Omelka, M. (2019), “Rank-based Inference Tools for Copula Regression, with Property and Casualty Insurance Applications,” Insurance: Mathematics and Economics, 89, 1–15. DOI: 10.1016/j.insmatheco.2019.08.001.
   Web of Science ®Google Scholar
• Curtin, T. R., Ingels, S., Wu, S., and Heuer, R. (2002), “Base-Year to Fourth Follow-Up Data File User’s Manual,” National Center for Education Statistics. Users Manual, July, 2002.
   Google Scholar
• Dziugaite, G. K., Roy, D. M., and Ghahramani, Z. (2015), “Training Generative Neural Networks via Maximum Mean Discrepancy Optimization,” in Proceedings of the Conference on Uncertainty in Artificial Intelligence.
   Google Scholar
• Embrechts, P., McNeil, A. J., and Straumann, D. (2002), “Correlation and Dependency in Risk Management: Properties and Pitfalls,” in Risk Management: Value at Risk and Beyond, ed. M. Dempster, pp. 176–223, Cambridge: Cambridge University Press.
   Google Scholar
• EPA (2021), “Air Quality System (aqs) api,” United States Environmental Protection Agency.
   Google Scholar
• Esipov, A. (2019), “2019 Ironman World Championship Results,” available at https://www.kaggle.com/andyesi/2019-ironman-world-championship-results/version/1.
   Google Scholar
• Frees, E. W., and Valdez, E. A. (2008), “Hierarchical Insurance Claims Modeling,” Journal of the American Statistical Association, 103, 1457–1469. DOI: 10.1198/016214508000000823.
   Web of Science ®Google Scholar
• Frees, E. W., and Wang, P. (2005), “Credibility Using Copulas,” North American Actuarial Journal, 9, 31–48. DOI: 10.1080/10920277.2005.10596196.
   Google Scholar
• Frees, E. W., and Wang, P. (2006), “Copula Credibility for Aggregate Loss Models,” Insurance: Mathematics and Economics, 38, 360–373.
   Web of Science ®Google Scholar
• Gijbels, I., Omelka, M., and Veraverbeke, N. (2015), “Estimation of a Copula When a Covariate Affects Only Marginal Distributions,” Scandinavian Journal of Statistics, 42, 1109–1126. DOI: 10.1111/sjos.12154.
   Web of Science ®Google Scholar
• He, W., and Lawless, J. F. (2005), “Bivariate Location-Scale Models for Regression Analysis, with Applications to Lifetime Data,” Journal of the Royal Statistical Society, Series B, 67, 63–78. DOI: 10.1111/j.1467-9868.2005.00488.x.
   Google Scholar
• Hofert, M., Prasad, A., and Zhu, M. (2021), “Quasi-Random Sampling for Multivariate Distributions via Generative Neural Networks,” Journal of Computational and Graphical Statistics, 30, 647–670. DOI: 10.1080/10618600.2020.1868302.
   Web of Science ®Google Scholar
• Howell, N. (1985), Demography of the Dobe! Kung, Routledge. https://tspace.library.utoronto.ca/handle/1807/17973 (2021-12-01).
   Google Scholar
• Kingma, D. P., and Welling, M. (2013), “Auto-Encoding Variational Bayes.”
   Google Scholar
• Li, Y., Swersky, K., and Zemel, R. (2015), “Generative Moment Matching Networks,” in International Conference on Machine Learning, pp. 1718–1727.
   Google Scholar
• McElreath, R. (2020), Statistical Rethinking: A Bayesian Course with Examples in R and STAN, Chapman and Hall/CRC. https://github.com/rmcelreath/rethinking/tree/master/data (2021-12-01).
   Google Scholar
• Mercer, J. (1909), “Xvi. Functions of Positive and Negative Type, and their Connection the Theory of Integral Equations,” Philosophical Transactions of the Royal Society of London, Series A, 209, 415–446.
   Google Scholar
• National Center for Education Statistics (2021) https://nces.ed.gov/ OnlineCodebook (2021-12-01).
   Google Scholar
• Nelsen, R. B. (2006), An Introduction to Copulas, New York: Springer-Verlag.
   Google Scholar
• Oakes, D., and Ritz, J. (2000), “Regression in a Bivariate Copula Model,” Biometrika, 87, 345–352. DOI: 10.1093/biomet/87.2.345.
   Web of Science ®Google Scholar
• Rémillard, B., and Scaillet, O. (2009), “Testing for Equality between Two Copulas,” Journal of Multivariate Analysis, 100, 377–386. DOI: 10.1016/j.jmva.2008.05.004.
   Web of Science ®Google Scholar
• Sklar, A. (1959), “Fonctions de répartition à n dimensions et leurs marges,” Publications de L’Institut de Statistique de L’Université de Paris, 8, 229–231.
   Google Scholar
• Song, P. X.-K. (2000), “Multivariate Dispersion Models Generated from Gaussian Copula,” Scandinavian Journal of Statistics, 27, 305–320.
   Web of Science ®Google Scholar