asymmetryCurve: Asymmetry curve based on depths
In depthproc: depthproc

Description Usage Arguments Details Author(s) References See Also Examples

Produces an asymmetry curve estimated from given data.

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asymmetryCurve(x, y = NULL, alpha = seq(0, 1, 0.01),
  method = "Projection", movingmedian = FALSE, name = "X", name_y = "Y",
  ...)

`x`	The data as a matrix or data frame. If it is a matrix or data frame, then each row is viewed as one multivariate observation.
`y`	Additional matrix of multivariate data.
`alpha`	An ordered vector containing indices of central regins used for asymmetry curve calculation.
`method`	Character string which determines the depth function used. The method can be "Projection" (the default), "Mahalanobis", "Euclidean", "Tukey" or 'LP'. For details see `depth.`
`movingmedian`	Logical. For default FALSE only one depth median is used to compute asymmetry norm. If TRUE - for every central area, a new depth median will be used - this approach needs much more time.
`name`	Name of set X - used in plot legend
`name_y`	Name of set Y - used in plot legend
`...`	Any additional parameters for function depth

For sample depth function D({x},{{{Z}}^{n}}) , {x}\in {{{R}}^{d}} , d≥ 2 , {Z}^{n}=\{{{{z}}_{1}},...,{{{z}}_{n}}\}\subset {{{R}}^{d}} , {{D}_{α }}({{{Z}}^{n}}) denoting α- central region, we can define the asymmetry curve AC(α )=≤ft( α ,≤ft\| {{c}^{-1}}(\{{\bar{z}}-med|{{D}_{α }}({{{Z}}^{n}})\}) \right\| \right)\subset {{{R}}^{2}} , for α \in [0,1] being nonparametric scale and asymmetry functional correspondingly, where c- denotes constant, {\bar{z}}- denotes mean vector, denotes multivariate median induced by depth function and vol- denotes a volume.

Asymmetrycurve takes uses function convhulln from package geometry for computing a volume of convex hull containing central region.

Daniel Kosiorowski, Mateusz Bocian, Anna Wegrzynkiewicz and Zygmunt Zawadzki from Cracow University of Economics.

Serfling R. J. Multivariate Symmetry and Asymmetry, Encyclopedia of Statistical Science, S Kotz, C.B. Read, N. Balakrishnan, B. Vidakovic (eds), 2nd, ed., John Wiley.

Liu, R.Y., Parelius, J.M. and Singh, K. (1999), Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion), Ann. Statist., 27, 783–858.

Chaudhuri, P. (1996), On a Geometric Notion of Quantiles for Multivariate Data, Journal of the American Statistical Association, 862–872.

Dyckerhoff, R. (2004), Data Depths Satisfying the Projection Property, Allgemeines Statistisches Archiv., 88, 163–190.

scaleCurve, depth

#EXAMPLE 1
require(MASS)
require(sn)
xi = c(0,0)
alpha <- c(2,-5)
Omega <- diag(2)*5

n = 500
X = mvrnorm(n, xi, Omega)  # normal distribution
Y = rmst(n, xi, Omega, alpha, nu=1)
asymmetryCurve(X,Y,name = "NORM",name_y = "S_T(2,-5,10)")


#EXAMPLE 2
data(under5.mort)
data(inf.mort)
data(maesles.imm)
data1990=cbind(under5.mort[,1],inf.mort[,1],maesles.imm[,1])
data2011=cbind(under5.mort[,22],inf.mort[,22],maesles.imm[,22])
as1990=asymmetryCurve(data1990,name='scale curve 1990')
as2011=asymmetryCurve(data2011,name='scale curve 2011')
figure=getPlot(as1990 %+% as2011)+ggtitle('Scale curves')
figure