expectile | R Documentation |

Expectiles are fitted to univariate samples with least asymmetrically weighted squares for asymmetries between 0 and 1.
For graphical representation an expectile - expectile plot is available. The corresponding functions `quantile`

, `qqplot`

and `qqnorm`

are mapped here for expectiles.

expectile(x, probs = seq(0, 1, 0.25), dec = 4) eenorm(y, main = "Normal E-E Plot", xlab = "Theoretical Expectiles", ylab = "Sample Expectiles", plot.it = TRUE, datax = FALSE, ...) eeplot(x, y, plot.it = TRUE, xlab = deparse(substitute(x)), ylab = deparse(substitute(y)), main = "E-E Plot", ...)

`x, y` |
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. |

`plot.it` |
logical. Should the result be plotted? |

`datax` |
logical. Should data values be on the x-axis? |

`xlab, ylab, main` |
plot labels. The xlab and ylab refer to the x and y axes respectively if |

`...` |
graphical parameters. |

In least asymmetrically weighted squares (LAWS) each expectile is fitted independently from the others. LAWS minimizes:

* S = ∑_{i=1}^{n}{ w_i(p)(x_i - μ(p))^2} *

with

* w_i(p) = p 1_{(x_i > μ(p))} + (1-p) 1_{(x_i < μ(p))} *.

*μ(p)* is determined by iteration process with recomputed weights *w_i(p)*.

Numeric vector with the fitted expectiles.

Fabian Otto-Sobotka

Carl von Ossietzky University Oldenburg

https://uol.de

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

`expectreg.ls`

, `quantile`

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)) eenorm(x)

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