Univariate Location and Scale Estimation.

DESCRIPTION:

Returns a list containing estimates of the location and the spread of the data. location.lms uses the exact algorithm of Rousseeuw and Leroy (1987, pages 169-170).

USAGE:

location.lms(xvec, minquan=floor(length(xvec)/2) 

REQUIRED ARGUMENTS:

xvec
a vector containing the observations of which the location has to be determined. Missing values ( NAs) and Infinite values ( Infs) are not accepted.

OPTIONAL ARGUMENTS:

minquan
the amount of data that is considered as a "half" (minus 1).

VALUE:

a list giving the solution. The components of the returned list are:
loc
an estimate for the location of the data.
scale
a scale estimate giving an idea about the length of the shortest half.

DETAILS:

Let n be the number of observations. The method of the shortest half estimates univariate location. The location estimator is defined as the midpoint of the "shortest" half of the data. The scale estimator is essentially the length of that half, as proposed by Rousseeuw and Leroy (1988). A "half" means minquan + 1 observations of the data points.

First the observations are ordered. The lengths of the successive halves are computed. (Note that not all halves have to be considered because the observations are ordered.) For the location estimate, the center of the shortest half is returned. If there are several shortest, the low median of their centers is returned. For the scale estimate the length (which is always unique) of the shortest half is returned.

The univariate location and scale estimator can be considered as a particular case of the general regression model. The method of the shortest half is a special case of lmsreg. Also the minimum volume ellipsoid estimator reduces to the shortest half in one dimension.

BACKGROUND:

This location estimator's breakdown value is 50%. That is, the estimate cannot be pulled arbitrarily far away without changing about half of the data.

REFERENCES:

Rousseeuw, P.J. and Leroy, A.M. (1987). Robust Regression and Outlier Detection. New York: Wiley.

Rousseeuw, P.J. and Leroy, A.M. (1988). A Robust Scale Estimator Based on the Shortest Half. Statistica Neerlandica, 42, 103-116.

SEE ALSO:

, .

EXAMPLES:

x <- c(90,93,86,92,95,83,75,40,88,80) 
sort(x) 
mean(x) 
median(x) 
location.lms(x)