Description Usage Arguments Details Value Author(s) See Also Examples
Weighted by L^p depth (outlyingness) multivariate location and scatter estimators.
1 | CovLP(x, pdim = 2, la = 1, lb = 1)
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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. |
pdim |
The parameter of the weighted L^pdim depth |
la |
parameter of a simple weight function w=a*x+b |
lb |
parameter of a simple weight function w=a*x+b |
Using depth function one can define a depth-weighted location and scatter estimators. In case of location estimator we have
L(F)={\int{{x}{{w}_{1}}(D({x},F))dF({x})}}/{{{w}_{1}}(D({x},F))dF({x})},
Subsequently, a depth-weighted scatter estimator is defined as
S(F)=\frac{\int{({x}-L(F)){{({x}-L(F))}^{T}}{{w}_{2}}(D({x},F))dF({x})}}{\int{{{w}_{2}}(D({x},F))dF({x})}},
where {{w}_{2}}(\cdot ) is a suitable weight function that can be different from {{w}_{1}}(\cdot ) .
The DepthProc package offers these estimators for weighted {L}^{p} depth. Note that L(\cdot ) and S(\cdot ) include multivariate versions of trimmed means and covariance matrices. Their sample counterparts take the form
{{T}_{WD}}({{{X}}^{n}})={∑\limits_{i=1}^{n}{{{d}_{i}}{{X}_{i}}}}/{∑\limits_{i=1}^{n}{{{d}_{i}}}} ,
DIS({{{X}}^{n}})=\frac{∑\limits_{i=1}^{n}{{{d}_{i}}≤ft( {{{X}}_{i}}-{{T}_{WD}}({{{X}}^{n}}) \right){{≤ft( {{{X}}_{i}}-{{T}_{WD}}({{{X}}^{n}}) \right)}^{T}}}}{∑\limits_{i=1}^{n}{{{d}_{i}}}},
where {{d}_{i}} are sample depth weights, {{w}_{1}}(x)={{w}_{2}}(x)=x .
loc: Robust Estimate of Location:
cov: Robust Estimate of Covariance:
Returns depth weighted covariance matrix.
Daniel Kosiorowski and Zygmunt Zawadzki from Cracow University of Economics.
depthContour
and depthPersp
for depth graphics.
1 2 3 4 5 6 7 | x = mvrnorm(n = 100, mu = c(0,0), Sigma = 3*diag(2))
cov_x = CovLP(x, 2, 1, 1)
# EXAMPLE 2
data(under5.mort,inf.mort,maesles.imm)
data1990 = na.omit(cbind(under5.mort[,1],inf.mort[,1],maesles.imm[,1]))
CovLP(data1990)
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