Computing trimmed measures of sherical location

Description

Computes a sample trimmed measure of location based on the spherical Tukey's depth. Supports data on the circle or on the sphere (for Circular median only).

Usage

1
strmeasure(P,sorted=FALSE,depths=NULL,alpha=0,method="Mean")

Arguments

P

The data as a vector, a matrix, a data frame or a list.

sorted

Logical; if TRUE, it indicates that the data given in first argument is sorted.

depths

An optionnal vector of the same length of P that contains the Tukey's depth of each data. The calculation of the depth is then skipped and the provided values are used instead.

alpha

An optionnal numeric value between 0 and 1 to compute the median on a trimmed region rather than on the whole dataset. The trimming keeps only those points with a depth greater than or equal to alpha. The default value of 0 computes the median from the maximum depth trimmed region (i.e. no trimming).

method

Character string which determines the measure used. method can be "Mean" (the default) to compute trimmed mean direction or "Tukey" (for circular sample only) to compute trimmed Tukey's median.

Details

This function returns a location estimate (Tukey's median or mean direction) of a sample truncated by Tukey's depth. For data on the circle, data must be expressed in polar coordinates as a angle in radians with values between 0 and . Data on the sphere can be expressed in Euclidean coordinates (n by 3 matrix) or in spherical coordinates (n by 2 matrix) where the first column contains θ and the second column φ. The type of coordinates is determined automatically based on the dimensions of the input.

While the option method="Tukey" supports only data on the circle, method="Mean" can also handle data on the sphere.

Value

If the input sample is on the circle, a numeric value between 0 and giving the trimmed measure. If the input sample is on the sphere, the trimmed measure in Euclidean coordinates.

Author(s)

Maxime Genest.

References

Liu, R.Y., Parelius, J.M. and Singh, K. (1999), Multivariate analysis by data depth: Descriptive statistics, graphics and inference (with discussion), Ann. Statist., 27, 783–858.

Mardia, K.V. and Jupp, E.J. (1999). Directional Statistics, Wiley.

See Also

sdepth for the calculation of the depth of a point, scontour for Tukey's spherical median.

Examples

1
2
3
4
5
6
7
## calculation of trimmed mean direction
set.seed(2011)
strmeasure(runif(30,min=0,max=2*pi),alpha=1/3,method="Mean")

## calculating of trimmed Tukey median
set.seed(2011)
strmeasure(runif(30,min=0,max=2*pi),alpha=1/3,method="Tukey")