findh {SOPIE}

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}

\hat h_9=\frac{1}{8}\sum _{i=1}^8{h_i}

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.

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)
findh(simdata,h=9,to=1)