expectile: Sample Expectiles

In expectreg: Expectile and Quantile Regression

Description

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.

Usage

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", ...)

Arguments

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 datax = TRUE.
...	graphical parameters.

Details

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).

Value

Numeric vector with the fitted expectiles.

Author(s)

Fabian Otto-Sobotka
Carl von Ossietzky University Oldenburg
http://www.uni-oldenburg.de

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

expectreg.ls, quantile

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))

eenorm(x)

Example output

Loading required package: parallel
Loading required package: mboost
Loading required package: stabs
This is mboost 2.8-1. See 'package?mboost' and 'news(package  = "mboost")'
for a complete list of changes.

Loading required package: BayesX
Loading required package: shapefiles
Loading required package: foreign

Attaching package: 'shapefiles'

The following objects are masked from 'package:foreign':

    read.dbf, write.dbf

Note: Function plotsurf depends on akima which has
 a restricted licence that explicitly forbids commercial use.
 akima is therefore disabled by default and may be enabled by
 akimaPermit(). Calling this function includes your agreement to
 akima`s licence restrictions.
       0     0.25      0.5     0.75        1 
 50.0000 108.5825 130.9574 150.7545 199.1000 
   0.01    0.02    0.05     0.1     0.2     0.5     0.8     0.9    0.95    0.98 
-1.7230 -1.4609 -1.1120 -0.8315 -0.5257  0.0080  0.5418  0.8406  1.1086  1.4331 
   0.99 
 1.6782 
$x
 [1] -1.668253149 -1.434743114 -1.292118765 -1.187796310 -1.104845757
 [6] -1.035590100 -0.975878113 -0.923204326 -0.875937451 -0.832954523
[11] -0.793448722 -0.756820355 -0.722611211 -0.690463048 -0.660090310
[16] -0.631261558 -0.603786495 -0.577506659 -0.552288607 -0.528018838
[21] -0.504599931 -0.481947582 -0.459988288 -0.438657518 -0.417898253
[26] -0.397659810 -0.377896883 -0.358568757 -0.339638658 -0.321073209
[31] -0.302841977 -0.284917085 -0.267272884 -0.249885676 -0.232733472
[36] -0.215795778 -0.199053421 -0.182488380 -0.166083654 -0.149823131
[41] -0.133691477 -0.117674041 -0.101756756 -0.085926062 -0.070168831
[46] -0.054472288 -0.038823956 -0.023211583 -0.007623090  0.007953491
[51]  0.023530073  0.039118566  0.054730939  0.070379271  0.086075814
[56]  0.101833045  0.117663738  0.133581024  0.149598460  0.165730114
[61]  0.181990637  0.198395363  0.214960404  0.231702761  0.248640455
[66]  0.265792659  0.283179867  0.300824068  0.318748960  0.336980192
[71]  0.355545641  0.374475740  0.393803866  0.413566793  0.433805236
[76]  0.454564501  0.475895271  0.497854565  0.520506913  0.543925821
[81]  0.568195590  0.593413642  0.619693478  0.647168541  0.675997293
[86]  0.706370031  0.738518194  0.772727338  0.809355705  0.848861506
[91]  0.891844433  0.939111309  0.991785096  1.051497083  1.120752740
[96]  1.203703293  1.308025748  1.450650097  1.684160132

$y
 [1] -1.7230 -1.4609 -1.3098 -1.1986 -1.1120 -1.0407 -0.9794 -0.9243 -0.8754
[10] -0.8315 -0.7911 -0.7541 -0.7200 -0.6879 -0.6576 -0.6290 -0.6017 -0.5754
[19] -0.5501 -0.5257 -0.5022 -0.4794 -0.4573 -0.4360 -0.4153 -0.3950 -0.3753
[28] -0.3561 -0.3372 -0.3188 -0.3007 -0.2830 -0.2654 -0.2481 -0.2311 -0.2143
[37] -0.1977 -0.1812 -0.1650 -0.1488 -0.1329 -0.1170 -0.1013 -0.0855 -0.0699
[46] -0.0543 -0.0387 -0.0232 -0.0076  0.0080  0.0235  0.0391  0.0548  0.0705
[55]  0.0862  0.1020  0.1179  0.1338  0.1499  0.1660  0.1823  0.1988  0.2154
[64]  0.2321  0.2491  0.2663  0.2836  0.3013  0.3191  0.3372  0.3556  0.3744
[73]  0.3936  0.4133  0.4335  0.4541  0.4751  0.4966  0.5188  0.5418  0.5654
[82]  0.5901  0.6158  0.6427  0.6711  0.7007  0.7323  0.7658  0.8017  0.8406
[91]  0.8829  0.9290  0.9808  1.0398  1.1086  1.1901  1.2933  1.4331  1.6782

expectreg documentation built on Aug. 24, 2019, 1:05 a.m.