CovLP function

CovLp

Weighted by $L ^ p$ 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 ${L} ^ {p} dim$ depth
• la: parameter of a simple weight function $w = ax + b$
• lb: parameter of a simple weight function $w = ax + b$

Returns

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

Subsequently, a depth-weighted scatter estimator is defined as

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

where ${{d}_{i}}$ are sample depth weights, ${{w}_{1}}(x) = {{w}_{2}}(x) = x$.

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)

See Also

depthContour and depthPersp for depth graphics.

Author(s)

Daniel Kosiorowski and Zygmunt Zawadzki from Cracow University of Economics.