shorth {parody} | R Documentation |
generalized length of shortest-half sample
shorth(x, Alpha=0.5)
x |
data vector, no NAs |
Alpha |
minimum fraction of data to be covered by scale estimator.
if Alpha == 0.5, the shorth is calculated
|
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 |
Rousseeuw and Leroy, Stat Neer (1988), Gruebel, Ann Stat (1988)