sce {isocir}

Sum of Circular Error

Description

This function calculates the distance between two q dimensional points, or between a point and a set of points, in the circular space.

Usage

sce(arg1, arg2, meanrl=1)

Arguments

arg1

vector with the values for the first point.

arg2

vector (or matrix) with the values for the second point (set of points).

meanrl

vector with the mean resultant lenght, by default 1.

Details

This function is useful to measure the circular error when an estimator is used to estimate an unknown q-dimensional parameter. It plays a role in the circular space similar to that of the mean squared error in the usual Euclidean space.

When arg2 is a vector:

SCE(arg1,arg2)=\sum_{i=1}^{q} r_{i} [1-\cos (arg1_{i}-arg2_{i})]

If arg1 and arg2 are just to q dimensional points, both arguments must be vectors with the same length and meanrl is not needed because r_i=1.

If arg2 is a mean vector coming from several replications, the corresponding mean resultant lengths (r_i) have to be introduced in the argument meanrl.

When arg2 is a matrix:

SCE(arg1,arg2)=\sum_{i=1}^{q}\sum_{k=1}^{n} [1-\cos (arg1_{i}-arg2_{ik})]

If arg2 is a matrix with the replications in its columns, meanrl is not needed as the mean resultant lengths are calculated internally.

Value

The value of the Sum of Circular Error.

Author(s)

Author(s): Sandra Barragán based on the SAS routine written by Miguel A. Fernández. Maintainer: <[e-mail]>

References

Mardia, K. and Jupp, P. (2000). Directional Statistics, Chichester: Wiley.

Rueda, C., Fernandez, M. A. and Peddada, S. D. (2009). Estimation of parameters subject to order restrictions on a circle with application to estimation of phase angles of cell-cycle genes. Journal of the American Statistical Association, 104, n485; pp 338–347. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC2742472/

Fernandez, M. A., Rueda, C. and Peddada, S. D. (2012). Identification of a core set of signature cell cycle genes whose relative order of time to peak expression is conserved across species, Nucl. Acids Res. 40, n7: pp 2823–2832. doi:10.1093/nar/gkr1077. https://academic.oup.com/nar/article/40/7/2823/1183140

See Also

CIRE, cond.test, mrl.

Examples

data(cirdata)
exampledata1 <- cirdata
exampledata2 <- (cirdata+(pi/4))
sce(exampledata1,exampledata2)