circ.kernel {SOPIE}

Circular Kernel Density Estimation

Description

This function is used to perform circular kernel density estimation on the sample data set in order to obtain the minimum points of the kernel density estimator.

Usage

circ.kernel(data, sp, to = 1, grid = 512, m = 1)

Arguments

data

the data vector from which the circular kernel density estimator is to be computed.

sp

a real value (0 < sp < 1) for the smoothing parameter to be used. This value can be obtained by using findh.

to

the value of the maximum domain of the data. Values will usually either be 1 or 2\pi.

grid

the number of equally spaced grid points at which the density is to be estimated.

m

the number of local minimum points included in the output.

Details

The Epanechnikov kernel function is used in the circular kernel density estimation. Circular kernel density estimation is perform according to the method proposed in 'Topics in circular statistics' (see references).

Value

a list containing the following components:

x

a vector of sorted x values that represents the equally-spaced grid points used during the kernel density estimation.

y

a vector of density-values of the circular kernel density estimator corresponding to x.

minimum

a vector of the kernel grid point(s) of lowest density derived from the circular kernel density estimator. The length of the vector will depend on the choice of m.

Author(s)

Willem Daniel Schutte

References

Hall P, Watson G, Cabrera J (1987). Kernel density estimation with spherical data. Biometrika, 74 (4), 751-762.
Jammalamadaka S, SenGupta A (2001). Topics in circular statistics. World Scientific Publishing Co. Pte. Ltd.
Schutte WD (2014). Nonparametric estimation of the off-pulse interval(s) of a pulsar light curve. Ph.D. thesis, North-West University. URL http://hdl.handle.net/10394/12199
Schutte WD, Swanepoel JWH (2016). SOPIE: an R package for the non-parametric estimation of the off-pulse interval of a pulsar light curve. Monthly Notices of the Royal Astronomical Society, 461, 627-640.
Sheather, S. & Jones, M. (1991). A reliable data-based bandwidth selection method for kernel density estimation, Journal of the Royal Statistical Society, Series B, 53:683-690.
Silverman, B. (1986). Density estimation for Statistics and Data analysis, Chapman and Hall. Taylor, C. (2008). Automatic bandwith selection for circular density estimation, Computational Statistics & Data Analysis, 52:3493-3500. Wand, M. & Jones, M. (1995). Kernel Smoothing, Chapman and Hall.

Examples

simdata<-von_mises_sim(n=5000,k=1,c=0.3,noise=0.2)
circ.kernel(simdata, findh(simdata), to = 1, grid = 512, m = 1)