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Parametric and semiparametric approaches for copula-based regression estimation

Year 2024, Volume: 53 Issue: 4, 1141 - 1157, 27.08.2024
https://doi.org/10.15672/hujms.1359072

Abstract

Based on the normality assumption on dependent variable, regression analysis is one of the most popular statistical techniques for studying the dependence between response and explanatory variables. However, violation of this assumption in the data makes regression analysis inappropriate in several real life situations. Copula is a powerful tool for modeling multivariate data and have recently been employed in regression analysis. The key concept behind copula-based regression approach is to formulate conditional expectation in terms of copula density and marginal distributions. In this paper, we explore parametric and semiparametric estimations of the copula-based regression function. The maximum likelihood (ML), inference functions for margins (IFM), and pseudo maximum likelihood (PML) techniques are adopted here for estimation purposes. Extensive numerical experiments are performed to illustrate the performance of the proposed copula-based regression estimators under specified and misspecified scenarios of copulas and marginals. Finally, two real data applications are also presented to demonstrate the performance of the considered estimators.

Ethical Statement

No potential conflict of interest was reported by thrauthor(s)

Supporting Institution

Department of Science and Technology (DST), Government of India

Project Number

IF 190682

References

  • [1] E.F. Acar, P. Azimaee and M.E. Hoque, Predictive assessment of copula models, Can. J. Stat. 47 (1), 8-26, 2019.
  • [2] A. Ahdika, D. Rosadi and A.R. Effendie, Conditional expectation formula of copulas for higher dimensions and its application, J. Math. Comput. Sci. 11 (4), 4877-4904, 2021.
  • [3] D. Berg, Copula goodness-of-fit testing: An overview and power comparison, Eur. J. Finance 15 (7-8), 675-701, 2009.
  • [4] T. Bouezmarni, F. Funke and F. Camirand Lemyre, Regression estimation based on Bernstein density copulas, Université de Sherbrooke, Submitted, 2014.
  • [5] B. Choroś, R. Ibragimov and E. Permiakova, Copula Estimation, Copula Theory and Its Applications, Springer, 2010.
  • [6] G.J. Crane and J. van der Hoek, Conditional expectation formulae for copulas, Aust. N. Z. J. Stat. 50 (1), 53-67, 2008.
  • [7] A.R. de Leon and B.Wu, Copula-based regression models for a bivariate mixed discrete and continuous outcome, Stat. Med. 30 (2), 175-185, 2011.
  • [8] J.B. de Long and L.H. Summers, Equipment investment and economic growth, Q. J. Econ. 106 (2), 445-502, 1991.
  • [9] H. Dette, R. Van Hecke and S. Volgushev, Some comments on copula-based regression, J. Am. Stat. Assoc. 109 (507), 1319-1324, 2014.
  • [10] ¨ O.K. Erdemir and M. Sucu, A modified pseudo-copula regression model for risk groups with various dependency levels, J. Stat. Comput. Simul. 92 (5), 1092-1112, 2022.
  • [11] C. Genest, K. Ghoudi and L.P. Rivest, A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika 82 (3), 543-552, 1995.
  • [12] C. Genest, W. Huang and J.M. Dufour, A regularized goodness-of-fit test for copulas, J. SFdS 154 (1), 64-77, 2013.
  • [13] C. Genest, B. Rémillard and D. Beaudoin, Goodness-of-fit tests for copulas: A review and a power study, Insur. Math. Econ. 44 (2), 199-213, 2009.
  • [14] S. Hamori, K. Motegi and Z. Zhang, Copula-based regression models with data missing at random, J. Multivariate Anal. 180, 1-23, 2020.
  • [15] M.S. Hofert, I. Kojadinovic, M. Maechler and J. Yan, Package "copula: Multivariate Dependence with Copulas", R package version: 1.1-3, 2023.
  • [16] J.P. Jaworski, F. Durante, W.K. Hardle and T. Rychlik, Copula Theory and Its Applications, 198, Springer, 2010.
  • [17] H. Joe, Dependence Modeling with Copulas, CRC Press, 2014.
  • [18] D. Kim and J.M. Kim, Analysis of directional dependence using asymmetric copulabased regression models, J. Stat. Comput. Simul. 84 (9), 1990-2010, 2014.
  • [19] G. Kim, M.J. Silvapulle and P. Silvapulle, Comparison of semiparametric and parametric methods for estimating copulas, Comput. Stat. Data. Anal. 51 (6), 2836-2850, 2007.
  • [20] I. Kojadinovic, J. Yan and M. Holmes, Fast large-sample goodness-of-fit tests for copulas, Statist. Sinica 21 (2), 841-871, 2011.
  • [21] N. Kolev and D. Paiva, Copula-based regression models: A survey, J. Statist. Plann. Inference 139 (11), 3847-3856, 2009.
  • [22] Y.K. Leong and E.A. Valdez, Claims prediction with dependence using copula models, Insurance: Mathematics and Economics, 2005.
  • [23] J.A. Nelder and R.W. Wedderburn, Generalized linear models, J. Roy. Statist. Soc. Ser. A 135 (3), 370-384, 1972.
  • [24] R.B. Nelsen, An Introduction to Copulas, 2nd ed., Springer, New York, 2007.
  • [25] H. Noh, A. El Ghouch and T. Bouezmarni, Copula-based regression estimation and inference, J. Amer. Statist. Assoc. 108 (502), 676-688, 2013.
  • [26] R.A. Parsa and S.A. Klugman, Copula regression, Variance 5, 45-54, 2011.
  • [27] K.W. Penrose, A. Nelson and A. Fisher, Generalized body composition prediction equation for men using simple measurement techniques, Med. Sci. Sports Exerc. 17 (2), 189, 1985.
  • [28] M. Pitt, D. Chan and R. Kohn, Efficient Bayesian inference for Gaussian copula regression models, Biometrika 93 (3), 537-554, 2006.
  • [29] A. Sheikhi, F. Arad and R. Mesiar, A heteroscedasticity diagnostic of a regression analysis with copula dependent random variables, Braz. J. Probab. Stat. 36 (2), 408- 419, 2022.
  • [30] M. Sklar, Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (3), 229-231, 1959.
  • [31] M.S. Smith and N. Klein, Bayesian inference for regression copulas, J. Bus. Econom. Statist. 39 (3), 712-728, 2021.
  • [32] E.A. Sungur, Some observations on copula regression functions, Comm. Statist. Theory Methods 34 (9-10), 1967-1978, 2005.
  • [33] H. Tsukahara, Semiparametric estimation in copula models, Canad. J. Statist. 33 (3), 357-375, 2005.
  • [34] P. Vellaisamy and A.K. Pathak, Copulas and regression models, J. Indian Statist. Assoc. 52 (1), 113-134, 2014.
Year 2024, Volume: 53 Issue: 4, 1141 - 1157, 27.08.2024
https://doi.org/10.15672/hujms.1359072

Abstract

Project Number

IF 190682

References

  • [1] E.F. Acar, P. Azimaee and M.E. Hoque, Predictive assessment of copula models, Can. J. Stat. 47 (1), 8-26, 2019.
  • [2] A. Ahdika, D. Rosadi and A.R. Effendie, Conditional expectation formula of copulas for higher dimensions and its application, J. Math. Comput. Sci. 11 (4), 4877-4904, 2021.
  • [3] D. Berg, Copula goodness-of-fit testing: An overview and power comparison, Eur. J. Finance 15 (7-8), 675-701, 2009.
  • [4] T. Bouezmarni, F. Funke and F. Camirand Lemyre, Regression estimation based on Bernstein density copulas, Université de Sherbrooke, Submitted, 2014.
  • [5] B. Choroś, R. Ibragimov and E. Permiakova, Copula Estimation, Copula Theory and Its Applications, Springer, 2010.
  • [6] G.J. Crane and J. van der Hoek, Conditional expectation formulae for copulas, Aust. N. Z. J. Stat. 50 (1), 53-67, 2008.
  • [7] A.R. de Leon and B.Wu, Copula-based regression models for a bivariate mixed discrete and continuous outcome, Stat. Med. 30 (2), 175-185, 2011.
  • [8] J.B. de Long and L.H. Summers, Equipment investment and economic growth, Q. J. Econ. 106 (2), 445-502, 1991.
  • [9] H. Dette, R. Van Hecke and S. Volgushev, Some comments on copula-based regression, J. Am. Stat. Assoc. 109 (507), 1319-1324, 2014.
  • [10] ¨ O.K. Erdemir and M. Sucu, A modified pseudo-copula regression model for risk groups with various dependency levels, J. Stat. Comput. Simul. 92 (5), 1092-1112, 2022.
  • [11] C. Genest, K. Ghoudi and L.P. Rivest, A semiparametric estimation procedure of dependence parameters in multivariate families of distributions, Biometrika 82 (3), 543-552, 1995.
  • [12] C. Genest, W. Huang and J.M. Dufour, A regularized goodness-of-fit test for copulas, J. SFdS 154 (1), 64-77, 2013.
  • [13] C. Genest, B. Rémillard and D. Beaudoin, Goodness-of-fit tests for copulas: A review and a power study, Insur. Math. Econ. 44 (2), 199-213, 2009.
  • [14] S. Hamori, K. Motegi and Z. Zhang, Copula-based regression models with data missing at random, J. Multivariate Anal. 180, 1-23, 2020.
  • [15] M.S. Hofert, I. Kojadinovic, M. Maechler and J. Yan, Package "copula: Multivariate Dependence with Copulas", R package version: 1.1-3, 2023.
  • [16] J.P. Jaworski, F. Durante, W.K. Hardle and T. Rychlik, Copula Theory and Its Applications, 198, Springer, 2010.
  • [17] H. Joe, Dependence Modeling with Copulas, CRC Press, 2014.
  • [18] D. Kim and J.M. Kim, Analysis of directional dependence using asymmetric copulabased regression models, J. Stat. Comput. Simul. 84 (9), 1990-2010, 2014.
  • [19] G. Kim, M.J. Silvapulle and P. Silvapulle, Comparison of semiparametric and parametric methods for estimating copulas, Comput. Stat. Data. Anal. 51 (6), 2836-2850, 2007.
  • [20] I. Kojadinovic, J. Yan and M. Holmes, Fast large-sample goodness-of-fit tests for copulas, Statist. Sinica 21 (2), 841-871, 2011.
  • [21] N. Kolev and D. Paiva, Copula-based regression models: A survey, J. Statist. Plann. Inference 139 (11), 3847-3856, 2009.
  • [22] Y.K. Leong and E.A. Valdez, Claims prediction with dependence using copula models, Insurance: Mathematics and Economics, 2005.
  • [23] J.A. Nelder and R.W. Wedderburn, Generalized linear models, J. Roy. Statist. Soc. Ser. A 135 (3), 370-384, 1972.
  • [24] R.B. Nelsen, An Introduction to Copulas, 2nd ed., Springer, New York, 2007.
  • [25] H. Noh, A. El Ghouch and T. Bouezmarni, Copula-based regression estimation and inference, J. Amer. Statist. Assoc. 108 (502), 676-688, 2013.
  • [26] R.A. Parsa and S.A. Klugman, Copula regression, Variance 5, 45-54, 2011.
  • [27] K.W. Penrose, A. Nelson and A. Fisher, Generalized body composition prediction equation for men using simple measurement techniques, Med. Sci. Sports Exerc. 17 (2), 189, 1985.
  • [28] M. Pitt, D. Chan and R. Kohn, Efficient Bayesian inference for Gaussian copula regression models, Biometrika 93 (3), 537-554, 2006.
  • [29] A. Sheikhi, F. Arad and R. Mesiar, A heteroscedasticity diagnostic of a regression analysis with copula dependent random variables, Braz. J. Probab. Stat. 36 (2), 408- 419, 2022.
  • [30] M. Sklar, Fonctions de répartition à n dimensions et leurs marges, Publ. Inst. Statist. Univ. Paris 8 (3), 229-231, 1959.
  • [31] M.S. Smith and N. Klein, Bayesian inference for regression copulas, J. Bus. Econom. Statist. 39 (3), 712-728, 2021.
  • [32] E.A. Sungur, Some observations on copula regression functions, Comm. Statist. Theory Methods 34 (9-10), 1967-1978, 2005.
  • [33] H. Tsukahara, Semiparametric estimation in copula models, Canad. J. Statist. 33 (3), 357-375, 2005.
  • [34] P. Vellaisamy and A.K. Pathak, Copulas and regression models, J. Indian Statist. Assoc. 52 (1), 113-134, 2014.
There are 34 citations in total.

Details

Primary Language English
Subjects Computational Statistics, Statistical Theory, Applied Statistics
Journal Section Statistics
Authors

Alam Ali 0009-0006-1273-0651

Ashok Pathak 0000-0002-0774-1202

Mohd Arshad 0000-0002-1877-4552

Project Number IF 190682
Early Pub Date August 5, 2024
Publication Date August 27, 2024
Published in Issue Year 2024 Volume: 53 Issue: 4

Cite

APA Ali, A., Pathak, A., & Arshad, M. (2024). Parametric and semiparametric approaches for copula-based regression estimation. Hacettepe Journal of Mathematics and Statistics, 53(4), 1141-1157. https://doi.org/10.15672/hujms.1359072
AMA Ali A, Pathak A, Arshad M. Parametric and semiparametric approaches for copula-based regression estimation. Hacettepe Journal of Mathematics and Statistics. August 2024;53(4):1141-1157. doi:10.15672/hujms.1359072
Chicago Ali, Alam, Ashok Pathak, and Mohd Arshad. “Parametric and Semiparametric Approaches for Copula-Based Regression Estimation”. Hacettepe Journal of Mathematics and Statistics 53, no. 4 (August 2024): 1141-57. https://doi.org/10.15672/hujms.1359072.
EndNote Ali A, Pathak A, Arshad M (August 1, 2024) Parametric and semiparametric approaches for copula-based regression estimation. Hacettepe Journal of Mathematics and Statistics 53 4 1141–1157.
IEEE A. Ali, A. Pathak, and M. Arshad, “Parametric and semiparametric approaches for copula-based regression estimation”, Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 4, pp. 1141–1157, 2024, doi: 10.15672/hujms.1359072.
ISNAD Ali, Alam et al. “Parametric and Semiparametric Approaches for Copula-Based Regression Estimation”. Hacettepe Journal of Mathematics and Statistics 53/4 (August 2024), 1141-1157. https://doi.org/10.15672/hujms.1359072.
JAMA Ali A, Pathak A, Arshad M. Parametric and semiparametric approaches for copula-based regression estimation. Hacettepe Journal of Mathematics and Statistics. 2024;53:1141–1157.
MLA Ali, Alam et al. “Parametric and Semiparametric Approaches for Copula-Based Regression Estimation”. Hacettepe Journal of Mathematics and Statistics, vol. 53, no. 4, 2024, pp. 1141-57, doi:10.15672/hujms.1359072.
Vancouver Ali A, Pathak A, Arshad M. Parametric and semiparametric approaches for copula-based regression estimation. Hacettepe Journal of Mathematics and Statistics. 2024;53(4):1141-57.