# 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

 1 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.