Cumulative Conditional Expectation Index

TL;DR

This paper explores the properties and estimation of the cumulative conditional expectation function within the copula framework, introducing Bernstein polynomial-based methods and analyzing their statistical characteristics.

Contribution

It provides a novel representation of CCEF using cumulative copula functions and develops Bernstein polynomial estimators with asymptotic analysis.

Findings

CCEF can be computed via the cumulative copula function.

Bernstein polynomial estimators for CCEF are asymptotically normal.

The paper discusses properties and applications of CCEF in copula models.

Abstract

In this paper we study the cumulative conditional expectation function (CCEF) in the copula context. It is shown how to compute CCEF in terms of the cumulative copula function, this natural representation allows to deduce some useful properties, for instance with applications to convex combination of copulas. We introduce approximations of CCEF based on Bernstein polynomial copulas. We introduce estimators for CCEF, which were constructed through Bernstein polynomial estimators for copulas. The estimators are asymptotically normal and biased for CCEF.