SOPIE (version 1.6)

findh: Calculate the Estimated Smoothing Parameter

Description

This function is used to obtain the estimated smoothing parameter \(\hat h\) that will be used in the circular kernel density estimator (see circ.kernel).

Usage

findh(data, h = 1, to = 1)

Arguments

data

the data vector from which to calculate the estimated smoothing parameter \(\hat h\) that will be used in the circular kernel density estimator.

h

integer value from 1 to 9, specifying the smoothing parameter to calculate according to the following table:

\(\hat h_1=1.06sn^{-1/5}\)

\(\hat h_2=1.06s_\circ n^{-1/5}\)

\(\hat h_3=1.06\bar{D}_\circ n^{-1/5}\)

\(\hat h_4=1.06|{D}_\circ|n^{-1/5}\)

\(\hat h_5=1.06{IQR}_\circ n^{-1/5}\)

\(\hat h_6=\frac{1.06}{1.349}{IQR}_\circ n^{-1/5}\)

\(\hat h_7=0.9s_\circ n^{-1/5}\)

\(\hat h_8=\frac{0.9}{1.349}{IQR}_\circ n^{-1/5}\)

to

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

Value

The function produces a single real value between 0 and 1, representing the rounded value (to 2 decimal places) of the estimating smoothing parameter.

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

# NOT RUN {
simdata<-von_mises_sim(n=5000,k=1,c=0.3,noise=0.2)
findh(simdata,h=9,to=1)
# }