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wle (version 0.9-91)

wle.vonmises: von Mises Weighted Likelihood Estimates

Description

Computes the weighted likelihood estimates for the parameters of a von Mises distribution: the mean direction and the concentration parameter.

Usage

wle.vonmises(x, boot = 30, group, num.sol = 1, raf = "HD", smooth, tol = 10^(-6), equal = 10^(-3), max.iter = 500, bias = FALSE, mle.bias = FALSE, max.kappa = 500, min.kappa = 0.01, use.smooth = TRUE, alpha = NULL, p = 2, verbose = FALSE, control.circular = list()) "print"(x, digits = max(3, getOption("digits") - 3), ...)

Arguments

x
a vector. The object is coerced to class circular.
boot
the number of starting points based on boostrap subsamples to use in the search of the roots.
group
the dimension of the bootstap subsamples.
num.sol
maximum number of roots to be searched.
raf
type of Residual adjustment function to be use:

raf="HD": Hellinger Distance RAF,

raf="NED": Negative Exponential Disparity RAF,

raf="SCHI2": Symmetric Chi-Squared Disparity RAF.

smooth
the value of the smoothing parameter.
tol
the absolute accuracy to be used to achieve convergence of the algorithm.
equal
the absolute value for which two roots are considered the same. (This parameter must be greater than tol).
max.iter
maximum number of iterations.
bias
logical, if TRUE, the estimate for kappa is computed with a bias corrected method. Default is FALSE, i.e. no bias correction.
mle.bias
logical, if TRUE a bias corrected method is used to estimate the concentration parameter for the initial values.
max.kappa
maximum value for the concentration parameter.
min.kappa
minimum value for the concentration parameter.
use.smooth
logical, if TRUE a smoothed model is used, default is TRUE.
alpha
if not NULL overrides the value of p. See the next argument p. This is a different parameterization, alpha=-1/2 provides Hellinger Distance RAF, alpha=-1 provides Kullback-Leibler RAF and alpha=-2 provides Neyman's Chi-Square RAF.
p
this parameter works only when raf="HD". p=2 provides Hellinger Distance RAF, p=-1 provides Kullback-Leibler RAF and p=Inf provides Neyman's Chi-Square RAF.
verbose
logical, if TRUE warnings are printed.
control.circular
the attribute of the resulting object (mu)
digits
integer indicating the precision to be used.
...
further parameters in print.wle.vonmises.

Value

Returns a list with the following components:
call
the match.call().
mu
the estimate of the mean direction or the value supplied. If num.sol > 1 then mu may have length greater than 1, i.e, one value for each root found.
kappa
the estimate of the concentration parameter or the value supplied. If num.sol > 1 then kappa may have length greater than 1, i.e, one value for each root found.
tot.weights
the sum of the weights divide by the number of observations, one value for each root found.
weights
the weights associated to each observation, one column vector for each root found.
f.density
the non-parametric density estimation.
m.density
the smoothed model.
delta
the Pearson residuals.
tot.sol
the number of solutions found.
not.conv
the number of starting points that does not converge after the max.iter iteration are reached.

Details

Parameters p and raf will be change in the future. See the reference below for the definition of all the RAF.

References

C. Agostinelli. Robust estimation for circular data. Computational Statistics & Data Analysis, 51(12):5867-5875, 2007.

See Also

circular, mle.vonmises.

Examples

Run this code

x <- c(rvonmises(n=50, mu=circular(0), kappa=10), rvonmises(n=5, mu=circular(pi/2), kappa=20))
wle.vonmises(x, smooth=20, group=5)

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