robLoc: Robust Estimate of Location

In revss: Robust Estimation in Very Small Samples

Robust Estimate of Location

Description

Compute the robust estimate of location for very small samples.

Usage

robLoc(x, scale = NULL, na.rm = FALSE, maxit = 80L, tol = sqrt(.Machine$double.eps))

Arguments

x	A numeric vector.
scale	The scale, if known, can be used to enhance the estimate for the location; defaults to unknown.
na.rm	If TRUE then NA values are stripped from x before computation takes place.
maxit	The maximum number of iterations; defaults to 80.
tol	The desired accuracy.

Details

Computes the M-estimator for location using the logistic \psi function of Rousseeuw & Verboven (2002, 4.1). If there are three or fewer entries, the function defaults to the median.

If the scale is known and passed through scale, the algorithm uses the suggestion in Rousseeuw & Verboven section 5 (2002), substituting the known scale for the mad.

If na.rm is TRUE then NA values are stripped from x before computation takes place. If this is not done then an NA value in x will cause mad to return NA.

The tolerance and number of iterations are similar to those in existing base R functions.

Rousseeuw & Verboven suggest using this function when there are 3–8 samples. It is implied that having more than 8 samples allows the use of more standard estimators.

Value

Solves for the robust estimate of location, T_n, which is the solution to

\frac{1}{n}\sum_{i = 1}^n\psi\left(\frac{x_i - T_n}{S_n}\right) = 0

where S_n is fixed at mad(x). The \psi-function selected by Rousseeuw & Verboven is:

\psi_{log}(x) = \frac{e^x - 1}{e^x + 1}

This is equivalent to 2 * plogis(x) - 1.

Author(s)

Avraham Adler [e-mail]

References

Rousseeuw, Peter J. and Verboven, Sabine (2002) Robust estimation in very small samples. Computational Statistics & Data Analysis, 40, (4), 741–758. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0167-9473(02)00078-6")}

See Also

median

Examples

robLoc(c(1:9))
x <- c(1,2,3,5,7,8)
robLoc(x)

revss documentation built on June 22, 2024, 9:39 a.m.