Parametric and semiparametric approaches for copula-based regression estimation

Yıl 2024, Cilt: 53 Sayı: 4, 1141 - 1157, 27.08.2024

Alam Ali , Ashok Pathak , Mohd Arshad

https://doi.org/10.15672/hujms.1359072

Öz

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.

Anahtar Kelimeler

Copula-based regression estimation, dependence modelling, regression function, inference function for margins (IFM), semiparametric inference

Etik Beyan

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

Destekleyen Kurum

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

Proje Numarası

IF 190682

Kaynakça

• [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.