CovLP: CovLp
In depthproc: depthproc

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

Weighted by L^p depth (outlyingness) multivariate location and scatter estimators.

1	CovLP(x, p = 1, a = 1, b = 1)

`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.
`p`	The parameter of the weighted L^p depth
`a`	parameter of a simple weight function w=a*x+b
`b`	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.

require(MASS)
 x = mvrnorm(n = 100, mu = c(0,0), Sigma = 3*diag(2))
 cov_x = CovLP(x,1,1,1)

 # EXAMPLE 2
 data(under5.mort,inf.mort,maesles.imm)
 data1990 = na.omit(cbind(under5.mort[,1],inf.mort[,1],maesles.imm[,1]))
 CovLP(data1990)