Cumulative conditional expectation index

Article type: Research Article

Authors: Fernández, Mariela^a | González-López, Verónica Andrea^{b; *}

Affiliations: [a] B3, Praça Antonio Prado, 48, São Paulo, CEP 01010-901, Brazil | [b] Department of Statistics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas, São Paulo, CEP 13083-859, Brazil

Correspondence: [*] Corresponding author: Verónica Andrea González-López, Department of Statistics, University of Campinas, Rua Sérgio Buarque de Holanda, 651, Campinas, São Paulo, CEP 13083-859, Brazil. E-mail: veronica@ime.unicamp.br.

Abstract: 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.

Keywords: Conditional tail expectation, copula distributions, cumulative conditional expectation, educational researchAMS 2010 subject classifications: primary 62H20, 62G05; secondary 62P25.

DOI: 10.3233/JCM-180796

Journal: Journal of Computational Methods in Sciences and Engineering, vol. 18, no. 2, pp. 387-403, 2018