CovLp

Source: R/CovarianceFunctions.R

Weighted by Lp depth (outlyingness) multivariate location and scatter estimators.

CovLP(x, pdim = 2, la = 1, lb = 1)

Arguments

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 Lpdim depth
la

parameter of a simple weight function w=ax+b
lb

parameter of a simple weight function w=ax+b

Value

loc: Robust Estimate of Location:

cov: Robust Estimate of Covariance:

Returns depth weighted covariance matrix.

Details

Using depth function one can define a depth-weighted location and scatter estimators. In case of location estimator we have L(F)=∫xw1(D(x,F))dF(x)/w1(D(x,F))dF(x)

Subsequently, a depth-weighted scatter estimator is defined as S(F)=∫(x−L(F))(x−L(F))Tw2(D(x,F))dF(x)∫w2(D(x,F))dF(x),
where w2(⋅) is a suitable weight function that can be different from w1(⋅).

The DepthProc package offers these estimators for weighted Lp depth. Note that L(⋅) and S(⋅) include multivariate versions of trimmed means and covariance matrices. Their sample counterparts take the form TWD(Xn)=n∑i=1diXi/n∑i=1di,

DIS(Xn)=n∑i=1di(Xi−TWD(Xn))(Xi−TWD(Xn))Tn∑i=1di,
where di are sample depth weights, w1(x)=w2(x)=x.

See also

depthContour and depthPersp for depth graphics.

Examples

# EXAMPLE 1
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)
#> 
#> Call:
#> CovLP(x = data1990)
#> -> Method:  Depth Weighted Estimator 
#> 
#> Robust Estimate of Location: 
#> [1]  49.7  41.9  83.0
#> 
#> Robust Estimate of Covariance: 
#>       [,1]    [,2]    [,3]  
#> [1,]  3010.1  1771.8  -499.6
#> [2,]  1771.8  1079.8  -295.4
#> [3,]  -499.6  -295.4   252.7