expectreg (version 0.25)

expectile: Expectile regression of additive models

Description

Expectiles are fitted to univariate samples with least asymmetrically weighted squares for asymmetries between 0 and 1.

Usage

expectile(x, probs = seq(0, 1, 0.25), dec = 4)

Arguments

x

Numeric vector of univariate observations.

probs

Numeric vector of asymmetries between 0 and 1 where 0.5 corresponds to the mean.

dec

Number of decimals remaining after rounding the results.

Value

• Numeric vector with the fitted expectiles.

Details

In least asymmetrically weighted squares (LAWS) each expectile is fitted independently from the others. LAWS minimizes: $S = \sum_{i=1}^{n}{ w_i(p)(x_i - \mu(p))^2}$ with $w_i(p) = p 1_{(x_i > \mu(p))} + (1-p) 1_{(x_i < \mu(p))}$. $\mu(p)$ is determined by iteration process with recomputed weights $w_i(p)$.

References

Sobotka F and Kneib T (2010) Geoadditive Expectile Regression Computational Statistics and Data Analysis, doi: 10.1016/j.csda.2010.11.015.

See Also

expectile.laws

Examples

data(dutchboys)

expectile(dutchboys[,3])

x = rnorm(1000)

expectile(x,probs=c(0.01,0.02,0.05,0.1,0.2,0.5,0.8,0.9,0.95,0.98,0.99))