mde.wrappednormal: Wrapped Normal Minimum Distance Estimates
In wle: Weighted Likelihood Estimation

Description Usage Arguments Details Value Author(s) References See Also Examples

Computes the minimum distance estimates for the parameters of a Wrapped Normal distribution: the mean direction and the concentration parameter (and the scale parameter).

mde.wrappednormal(x, bw, mu = NULL, rho = NULL, sd = NULL,
  alpha = NULL, p = 2, tol = 1e-05, n = 512, from = circular(0),
  to = circular(2 * pi), lower = NULL, upper = NULL,
  method = "L-BFGS-B", lower.rho = 1e-06, upper.rho = 1 - 1e-06,
  min.sd = 0.001, K = NULL, min.k = 10, control.circular = list(), ...)
## S3 method for class 'mde.wrappednormal'
print(x, digits = max(3, getOption("digits") - 3), ...)

`x`	a vector. The object is coerced to class `circular`.
`bw`	the value of the smoothing parameter.
`mu`	initial value for the mean direction. Default: maximum likelihood estimate.
`rho`	initial value for the concentration parameter. Default: maximum likelihood estimate.
`sd`	initial value for the standard deviation parameter. This value is used only if `rho` is `NULL`. Default: maximum likelihood estimate.
`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, `alpha=-1` provides Kullback-Leibler distance and `alpha=-2` provides Neyman's Chi-Square distance.
`p`	`p=2` provides Hellinger distance, `p=-1` provides Kullback-Leibler distance and `p=Inf` provides Neyman's Chi-Square distance. It is ignored if `alpha` is not `NULL`.
`tol`	the absolute accuracy to be used to achieve convergence of the algorithm. This argument is passed to the function which determined the Maximum Likelihood estimates of the parameters. See `mle.wrappednormal`.
`n`	number of points used to approximate the density.
`from`	from which point in the circle the density is approximate.
`to`	to which point in the circle the density is approximate.
`lower`	a 2 elements vector passed to `optim` used to constrained optimization. First element for the mean direction, second element for the concentration.
`upper`	a 2 elements vector passed to `optim` used to constrained optimization. First element for the mean direction, second element for the concentration.
`method`	passed to `optim`.
`lower.rho`	if `lower` is `NULL` this parameter is used to constrained optimization for the concentration parameter.
`upper.rho`	if `upper` is `NULL` this parameter is used to constrained optimization for the concentration parameter.
`min.sd`	minimum value for the `sd` parameter. This argument is passed to the function which determined the Maximum Likelihood estimates of the parameters. See `mle.wrappednormal`.
`K`	number of elements used to approximate the density of the wrapped normal.
`min.k`	minimum number of elements used to approximate the density of the wrapped normal.
`control.circular`	the attribute of the resulting object (`mu`)
`digits`	integer indicating the precision to be used.
`...`	further parameters in `print.mde.wrappednormal`.

The distance from an estimated density (by the non parametric kernel density estimator) and the model is evaluated by simple rectangular approximation. optim is used to performs minimization.

Returns a list with the following components:

`call`	the match.call().
`mu`	the estimate of the mean direction.
`rho`	the estimate of the concentration parameter.
`sd`	the estimate of the standard deviation parameter.
`dist`	the distance between the estimated density and the model.
`data`	the original supplied data converted in radians, clockwise and zero at 0.
`x`	the 'n' coordinates of the points where the density is estimated.
`y`	the estimated density values.
`k`	the density at the model.

Claudio Agostinelli

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

circular, mle.wrappednormal and wle.wrappednormal.

set.seed(1234)
x <- c(rwrappednormal(n=200, mu=circular(0), sd=0.6),
  rwrappednormal(n=20, mu=circular(pi/2), sd=0.1))
res <- mde.wrappednormal(x, bw=0.08, mu=circular(0), sd=0.6)
res
plot(circular(0), type='n', xlim=c(-1, 1.75), shrink=1.2)
lines(circular(res$x), res$y)
lines(circular(res$x), res$k, col=2)
legend(1,1.5, legend=c('estimated density', 'MDE'), lty=c(1, 1), col=c(1, 2))