robustX: reclas – R documentation

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reclas

Recursive Robust Median-like Location and Scale

Description

Calculate an estimate of location, asymptotically equivalent to the median, and an estimate of scale equal to the MEAN absolute deviation. Both done recursively.

Usage

reclas(y, b = 0.2, mfn = function(n) 0.1 * n^(-0.25),
     nstart = 30, m0 = median(y0),
     scon=NULL, updateScale = is.null(scon))

Arguments

`y`	numeric vector of i.i.d. data whose location and scale parameters are to be estimated.
`b`	numeric tuning parameter (default value equal to that used by Holst, 1987).
`mfn`	a `function` of the index of the data which must be positive and and tend to 0 as the index tends to infinity. The default function is that used by Holst, 1987.
`nstart`	number of starting values: Starting values for the algorithm are formed from the first `nstart` values of `y`. The default value is that used in Cameron and Turner, 1993.
`m0`	value for the initial approximate median; by default, the `median` of the first `nstart` observations.
`scon`	value for the scale parameter `s`, a `function` or `NULL`. When `NULL`, as by default, the scale is initialized to the mean of the absolute differences between the first `nstart` y values and `m0`. If scon is a function, the initial scale is set to `scon(y0, m0)`, where `y0` is the vector of the first `nstart` y values. Note that `scon` also determines the default for `updateScale`.
`updateScale`	a logical indicating if the scale, initialized from `scon` should be updated in each iteration. Otherwise, the the scale is held constant throughout and the algorithm becomes equivalent to the algorithm of Holst.

Value

An S3 “object” of class "reclas"; simply a list with entries

`locn`	the successive recursive estimates of location. The first `nstart - 1` of these are `NA`.
`scale`	the successive recursive estimates of scale if `updateScale` is true; otherwise the constant value used for the scale.
`updateScale`	the same as the function argument.
`call`	the function call, i.e., `match.call`.

There is a plot method for "reclas", see the examples.

Author(s)

r.turner@auckland.ac.nz http://www.stat.auckland.ac.nz/~rolf

Extensions by Martin Maechler (scon as function; updateScale, plot()).

References

Cameron, Murray A. and Turner, T. Rolf (1993). Recursive location and scale estimators. Commun. Statist. — Theory Meth. 22(9) 2503–2515.

Holst, U. (1987). Recursive estimators of location. Commun. Statist. — Theory Meth. 16 (8) 2201–2226.

Examples

set.seed(42)
y <- rt(10000, df = 1.5) # not quite Gaussian ...
z1 <- reclas(y)
z3 <- reclas(y, scon= 1  ) # correct fixed scale
z4 <- reclas(y, scon= 100) # wrong fixed scale
z2 <- reclas(y, # a more robust initial scale:
           scon = function(y0, m0) robustbase::Qn(y0 - m0),
           updateScale = TRUE) # still updated

## Visualizing -- using the plot() method for "reclas":
M <- median(y) ; yl <- c(-1,1)* 0.5
OP <- par(mfrow=c(2,2), mar=.1+c(3,3,1,1), mgp=c(1.5, .6, 0))
 plot(z1, M=M, ylim=yl)
 plot(z2, M=M, ylim=yl)
 plot(z3, M=M, ylim=yl)
 plot(z4, M=M, ylim=yl)
par(OP)

robustX

'eXtra' / 'eXperimental' Functionality for Robust Statistics

v1.2-4

GPL (>= 2)

Authors

Werner Stahel, Martin Maechler [aut, cre] (<https://orcid.org/0000-0002-8685-9910>) and potentially others

Initial release

2019-02-25