esreg (version 0.3.1)

esreg_twostep: Two Step Quantile and Expected Shortfall Regression

Description

Estimates the expected shortfall in two steps. First a linear quantile regression, then a weighted least squares regression (see the Oracle estimator in the references for a brief explanation). This estimator is much faster than the joint estimator esreg. However, the estimates are often less precise and it is recommended primarily if one needs estimates quickly.

Usage

esreg_twostep(formula, data, alpha)

Arguments

formula

Formula object, e.g.: y ~ x1 + x2 + ...

data

data.frame that holds the variables. Can be missing.

alpha

Probability level

References

A Joint Quantile and Expected Shortfall Regression Framework

See Also

vcov.esreg_twostep for the covariance estimation and summary.esreg_twostep for a summary of the regression results

Examples

# NOT RUN {
# Simulate data (DGP-(2) in the linked paper)
set.seed(0)
x <- rchisq(2000, df=1)
y <- -x + (1 + 0.5 * x) * rnorm(1000)

# True quantile and expected shortfall regression parameters (for alpha=0.025)
alpha=0.025
true_pars <- c(-1.959964, -1.979982, -2.337803, -2.168901)

# Joint estimator
fit_joint <- esreg(y ~ x, alpha=alpha)

# Two-step estimator
fit_twostep <- esreg_twostep(y ~ x, alpha=alpha)

# Compare the estimates
print(rbind(Truth=true_pars, Joint=coef(fit_joint), `Two-Step`=coef(fit_twostep)))

# ... and the estimation times
print(c(Joint=fit_joint$time, `Two Step`=fit_twostep$time))
# }