Algorithm A is an implementation of Huber's location and scale estimate with iterated scale.
numeric vector or array of values.
Tuning factor; Winsorisation occurs ar k standard deviations.
a logical value indicating whether
Convergence tolerance Iteration continues until the relative
change in estimated sd drops below
Maximum number of iterations permitted.
Controls information displayed during iteration; see Details.
Algorithm A is the robust estimate of location described in ISO 5725-5:1998. It proceeds by winsorisation and re-estimation of scale and location.
k controls the point at which values are Winsorised
and hence controls the efficiency. At
k=1.5, the value chosen by
ISO 5725, the estimator has asymptotic efficiency at the Normal of 0.964.
With iterated estimate of scale and
k=1.5, the estimator has a
breakdown point of about 30
The convergence criterion for Algorithm A is not specified in ISO 5725-5:1998.
The criterion chosen here is reasonably stringent but the results will differ
from those obtained using other choices. Use
verbose=2 to check the
effect of different tolerance or maximum iteration count.
verbose is non-zero, the current iteration number
and estimate are printed; if
verbose>1, the current set
of truncated values w is also printed.
Robust estimate of location
Robust estimate of scale
Algorithm A uses the corrected median absolute deviation as the initial
estimate of scale; an error is returned if the resulting scale estimate is
zero, which can occur with over 50% of the data set equal.
the robustbase package uses an alternative scale estimate in these
Algorithm A is identical to Huber's estimate with variable scale.
The implementation here differs from
hubers from MASS in:
hubers allows prior specification of fixed scale (which provides higher breakdown if chosen properly) or location
the option of verbose output in
a maximum iteration option in
the convergence criterion; hubers converges on changes in
whilst this implementation of Algorithm A converges on changes in
Internally, Algorithm A multiplies by a correction factor for
standard deviation whilst
hubers divides by a correction factor
applied to the variance; the actual correction to
s is identical.
The principal reasons for providing an implementation in the metRology package are i) to ensure a close implementation of the cited Standard irrespective of other package developments (though the MASS implementation has proved very stable) and ii) to make the implementation easy to recognise for users of the ISO standard.
S L R Ellison firstname.lastname@example.org
ISO 5725-5:1998 Accuracy (trueness and precision) of measurement methods and results - Part 5: Alternative methods for the determination of the precision of a standard measurement method
Maronna R A, Martin R D, Yohai V J (2006) Robust statistics - theory and methods. Jhn Wiley and Sons, West Sussex, England.
1 2 3 4 5 6 7
Attaching package: 'metRology' The following objects are masked from 'package:base': cbind, rbind 0: mu=20.300000; s=0.948864 1: mu=20.387222; s=0.984891 2: mu=20.406605; s=1.008644 3: mu=20.410912; s=1.025393 4: mu=20.411869; s=1.037324 5: mu=20.412082; s=1.045860 6: mu=20.412129; s=1.051985 7: mu=20.412140; s=1.056389 8: mu=20.412142; s=1.059559 9: mu=20.412143; s=1.061844 10: mu=20.412143; s=1.063492 11: mu=20.412143; s=1.064682 12: mu=20.412143; s=1.065540 13: mu=20.412143; s=1.066160 14: mu=20.412143; s=1.066608 15: mu=20.412143; s=1.066931 16: mu=20.412143; s=1.067165 17: mu=20.412143; s=1.067333 18: mu=20.412143; s=1.067455 $mu  20.41214 $s  1.067455
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