shorth: one-dimensional MVE (min. vol. ellipsoid)

In parody: Parametric And Resistant Outlier DYtection

Description

generalized length of shortest-half sample

Usage

shorth(x, Alpha=0.5)

Arguments

x	data vector, no NAs
Alpha	minimum fraction of data to be covered by scale estimator. if Alpha == 0.5, the shorth is calculated

Value

a list, say L, with components

shorth	a 2-vector with endpoints of the shortest Alpha-sample
length.shorth	see previous return component L$shorth[2]-L$shorth[1]
midpt.shorth	mean(L[["shorth"]])
meanshorth	mean of values in the shorth, studied by Andrews et al (1972) as a location estimator
correction.parity.dep	correction factor to be applied to achieve approximate unbiasedness and diminish small-sample parity dependence; L["shorth"]] * L[["correction"]] is approximately unbiased for the Gaussian standard deviation, for 0 < Alpha < 1.
bias.correction.gau.5	correction factor to be applied along with correction.parity.dep when Alpha = .5; empirically derived bias correction useful for 10 < N < 2000 and possibly beyond. To use, divide: (L[["shorth"]] * L[["correction"]] / L[["bias.corr"]]) is approximately unbiased for Gaussian standard deviation, when Alpha=.5.
Alpha	coverage fraction used

References

Rousseeuw and Leroy, Stat Neer (1988), Gruebel, Ann Stat (1988)

parody documentation built on Nov. 8, 2020, 7:50 p.m.