Description Usage Arguments Details Value Author(s) See Also Examples
View source: R/CovarianceFunctions.R
Weighted by L ^ p depth (outlyingness) multivariate location and scatter estimators.
1 | CovLP(x, pdim = 2, la = 1, lb = 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. |
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 |
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 8 | # 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)
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