In this paper we introduce approximations of the cumulative conditional expectation function (CCEF) based on Bernstein polynomial copulas. These approximations converge pointwise and uniformly to CCEF. In addition some examples of the behavior of these approximations are shown. We also built estimators for the CCEF, which were constructed through Bernstein polynomial estimators for copulas. It is shown that the estimators are asymptotically normal and biased for the CCEF. We exemplify the use of these estimators through real data from the educational field.
FernándezM. and González-LópezV.A., A Bayesian approach for convex combination of two Gumbel-Barnett copulas, in: AIP Conference Proceedings, 1558, 2013, pp. 1491–1494.
2.
FernándezM. and González-LópezV.A., A copula model to analyze minimum admission scores, in: AIP Conference Proceedings, 1558, 2013, pp. 1479–1482.
3.
FernándezM. and González-LópezV.A., Bounds for the cumulative conditional expectation function, in: AIP Conference Proceedings, 1648, 2015, 060002.
4.
FernándezM. et al., A note on conjugate distributions for copulas, Mathematical Methods in the Applied Sciences38 (2014), 4797–4803.
5.
HuL., Dependence patterns across financial markets: a mixed copula approach, Applied Financial Economics16 (2006), 717–729.
6.
HuaL. and JoeH., Strength of tail dependence based on conditional tail expectation, Journal of Multivariate Analysis123 (2014), 143–159.
7.
JanssenP. et al., Large sample behavior of the Bernstein copula estimator, Journal of Statistical Planning and Inference142 (2012), 1189–1197.
8.
JanssenP. et al., A note on the asymptotic behavior of the Bernstein estimator of the copula density, Journal of Multivariate Analysis124 (2014), 480–487.
9.
KimD. and KimJ.M., Analysis of directional dependence using asymmetric copula-based regression models, Journal of Statistical Computation and Simulation84(9) (2013), 1990–2010.
10.
LiX. et al., Strong approximations of copulas, Journal of Mathematical Analysis and Applications225 (1998), 608–623.
11.
MuddapurM.V., A Remark on the Paper “A Note on Directional Dependence in Regression Setting” By Engin A. Sungur, Communications in Statistics – Theory and Methods37(3) (2008), 386–387.
12.
NelsenR., An Introduction to Copulas, Lecture Notes in Statistics 139, Springer-Verlag, 2006.
13.
SancettaA. and SatchellS., The Bernstein copula and its applications to modeling and approximations of multivariate distributions, Econometric Theory20 (2004), 535–562.
14.
SungurE.A., A note on directional dependence in regression setting, Communications in Statistics – Theory and Methods34(9–10) (2005), 1957–1965.
15.
SungurE.A., Some Observations on Copula Regression Functions, Communications in Statistics – Theory and Methods34(9–10) (2005), 1967–1978.
16.
Van der VaartA.W., Asymptotic Statistics, Cambridge University Press, 2000.
17.
VracM. et al., Copula analysis of mixture models, Computational Statistics27 (2012), 427–457.
