FastQn {robcor}

Robust, Efficient and Fast Scale Estimate

Description

Compute the robust scale estimator FastQn, an efficient alternative to the MAD, a fast alternative to the Qn.

Usage

FastQn(x, center = median(x), scale = mad(x, center))

fqn(x, center = median(x), scale = mad(x, center))

s_FastQn(x, mu.too = FALSE, center = median(x), ...)

Arguments

x

numeric vector of observations.

center

optionally, the center: defaults to the median.

scale

optionally, the basic scale: defaults to the median absolute deviation.

mu.too

logical indicating if the center should also be returned for s_FastQn().

...

potentially further arguments for s_FastQn() passed to FastQn().

Details

This function computes one-step M-estimate of scale based on provided robust estimate (defaults to the MAD). It gives 50% breakdown point and Gaussian efficiency about 80%.

The fqn function is a shorter alias, like sd and mad.

Value

FastQn() returns a number, the FastQn robust scale estimator.

s_FastQn(x, mu.too=TRUE) returns a length-2 vector with location and scale; this is typically only useful for covOGK(*, sigmamu = s_FastQn) or robcor(*, scaler = s_FastQn).

Author(s)

Paul Smirnov <[e-mail]>

References

Smirnov, P. O., Shevlyakov, G. L. (2010). On Approximation of the Qn-Estimate of Scale by Fast M-Estimates. In Book of Abstracts: International Conference on Robust Statistics (ICORS 2010) (pp. 94-95). Prague, Czech Republic.

See Also

mad, Qn.

Examples

set.seed(153)
x <- sort(c(rnorm(80), rt(20, df = 1)))
s_FastQn(x, mu.too=TRUE)
FastQn(x)