invert_cvar: Inverting 1 - conditional CDF

In ygeunkim/ceshat: Nonparametric Estimation of Conditional Expected Shortfall

Description

This function computes true CVaR given true conditional CDF.

Usage

invert_cvar(p = 0.95, cdf, x, lower = -1, upper = 1)

Arguments

p	Upper tail probability. 0.95, by default.
cdf	conditional cdf given x. Function of (y, x)
x	conditional information variable x
lower	lower value to be primarily searched
upper	upper value to be primarily searched

Details

Note that

\hat{nu}_p(x) = \hat{S}_c^{-1}(p \mid x)

where

\hat{S}(y \mid x)_c(y \mid x) = 1 - \hat{F}_c(y \mid x)

Inverting can be done by finding

\inf \{ y : F(y \mid x) ≥ 1 - p \}

When finding the minimum, firstly find in (lower, upper). But the answer can be out of this bound. These arguments just set the primary interval, not the final one.

Value

CVaR value for each x

References

Cai, Z., & Wang, X. (2008). Nonparametric estimation of conditional VaR and expected shortfall. Journal of Econometrics, 147(1), 120-130.

ygeunkim/ceshat documentation built on Dec. 16, 2019, 12:39 p.m.