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Semi-parametric order-based generalized multivariate regression

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  • Kharratzadeh, Milad
  • Coates, Mark

Abstract

In this paper, we consider a generalized multivariate regression problem where the responses are some functions of linear transformations of predictors. We assume that these functions are strictly monotonic, but their form and parameters are unknown. We propose a semi-parametric estimator based on the ordering of the responses which is invariant to the functional form of the transformation function as long as it is strictly monotonic. We prove that our estimator, which maximizes the rank similarity between responses and linear transformations of predictors, is a consistent estimator of the true coefficient matrix. We also identify the rate of convergence and show that the squared estimation error decays with a rate of o(1/n). We then propose a greedy algorithm to maximize the highly non-smooth objective function of our model and examine its performance through extensive simulations. Finally, we compare our algorithm with traditional multivariate regression algorithms over synthetic and real data.

Suggested Citation

  • Kharratzadeh, Milad & Coates, Mark, 2017. "Semi-parametric order-based generalized multivariate regression," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 89-102.
    • Handle: RePEc:eee:jmvana:v:156:y:2017:i:c:p:89-102
    DOI: 10.1016/j.jmva.2017.01.012
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    1. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    2. Xia, Yingcun & Härdle, Wolfgang, 2006. "Semi-parametric estimation of partially linear single-index models," Journal of Multivariate Analysis, Elsevier, vol. 97(5), pages 1162-1184, May.
    3. Ming Yuan & Ali Ekici & Zhaosong Lu & Renato Monteiro, 2007. "Dimension reduction and coefficient estimation in multivariate linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(3), pages 329-346, June.
    4. Han, Aaron K., 1987. "Non-parametric analysis of a generalized regression model : The maximum rank correlation estimator," Journal of Econometrics, Elsevier, vol. 35(2-3), pages 303-316, July.
    5. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-1057, September.
    6. Milton Friedman & L. J. Savage, 1948. "The Utility Analysis of Choices Involving Risk," Journal of Political Economy, University of Chicago Press, vol. 56(4), pages 279-279.
    7. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    8. Radchenko, Peter, 2015. "High dimensional single index models," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 266-282.
    9. Robert Tibshirani, 2011. "Regression shrinkage and selection via the lasso: a retrospective," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(3), pages 273-282, June.
    10. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
    11. Abrevaya, Jason, 2003. "Pairwise-Difference Rank Estimation of the Transformation Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 21(3), pages 437-447, July.
    12. Lisha Chen & Jianhua Z. Huang, 2012. "Sparse Reduced-Rank Regression for Simultaneous Dimension Reduction and Variable Selection," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1533-1545, December.
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