Confidence band for expectation dependence with applications

Abstract

Motivated by the applications of the concept of expectation dependence in economics and finance, we propose a method to construct uniform confidence band for expectation dependence. It is derived based on Hoeffding's inequality. Our proposed confidence band can be explicitly expressed and thus it is very easy to implement. Our method has applications to demand for a risky asset and first-order risk aversion problems. Simulations suggest our proposed confidence interval can control the coverage probabilities very well, and the average lengths are very short. Two empirical applications are presented to illustrate the usefulness of the constructed confidence band of expectation dependence.

Testing for more positive expectation dependence with application to model comparison

“…Tests for expectation dependance have been proposed in Zhu et al (2016), Cmiel and Ledwina (2017) and Linton et al (2018). Guo and Li (2016) proposed a method to construct uniform confidence band for quantities defining expectation dependence, derived from Hoeffding's inequality. In this paper, we design a testing procedure for comparing the strength of expectation dependence of Y on Z 1 and on Z 2 .…”

Validation of positive expectation dependence

“…Denuit and Mesfioui [14] provided some further insight into this problem. Moreover, recent work by Denuit et al [13] and Guo and Li [21] gave an excellent discussion of a wide range of further applications of (1.1). Guo and Li [21] concluded that expectation dependence is a key concept in many economic and financial studies.…”

“…Their approach is to estimate both sides of (1.1) and to reject the hypothesis of positive expectation dependence when the supremum (over the values of x) of the estimates of the differences of the form E(Y |X ≤ x) − EY is too large. This approach was recently advanced by Guo and Li [21], who provided confidence bounds for the curve…”