reclas {robustX}

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)

[e-mail] 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)