bw.AA | R Documentation |
Smoothing selectors for the circular kernel density (and its derivatives) estimator. This function implements the l-stage solve-the-equation and direct plug-in smoothing selector.
bw.AA(x,deriv.order=0,method = c("ste","dpi"),nstage=2,kernel="vonmises",M=NULL, commonkappa=TRUE,Q1=NULL,Q2=NULL,lower=NULL,upper=NULL,tol=NULL, approximate=NULL)
x |
Data from which the smoothing parameter is to be computed. The object is coerced to class |
deriv.order |
Derivative order. Default |
method |
Either |
nstage |
Number of stages in the plug-in smoothing parameter. Default |
kernel |
A character string giving the smoothing kernel to be used. This must be one of |
M |
Integer indicating the number of components in the von Mises mixture at stage 0. If |
commonkappa |
Logical; if |
Q1 |
Vector of constants related to the kernel to derive the explicit expression of the optimal smoothing parameters of the density functionals. Its value is provided by default when using the |
Q2 |
Constant related to the kernel to derive the explicit expression of the optimal smoothing parameters of the density derivative. Its value is provided by default when using the |
lower, upper |
For method |
tol |
For method |
approximate |
For method |
By default, this function computes the solve-the-equation plug-in rule for circular kernel density estimation. If method="dpi"
, this function computes the direct plug-in rule.
At stage 0, a mixture of von Mises is employed for computing the rule of thumb. The reason for employing a mixture model is that the von Mises estimates a uniform density when the true density model is k-fold rotational symmetric. Thus, in that case, the density functional estimator would be close to zero.
The number of components in the mixture is controlled with M
. By default, a von Mises density (M=1
) is employed in method="ste"
. For method="dpi"
, by default, the number of components in the mixture is selected using the Akaike Information Criterion, by comparing a mixture of 1 to 5 components. For simplicity, by default, the same concentration parameter is employed in all the components. This may be changed by setting commonkappa=F
.
For method="ste"
, the minimum number of stages is two (nstage=2
). Otherwise, the solve-the-equation rule cannot be computed. A rule of thumb can be computed with method="dpi"
and nstage=0
.
Value of the smoothing parameter (mean resultant length). When the kernel is vonmises
the bandwidth is equal to the concentration parameter.
Jose Ameijeiras-Alonso.
Ameijeiras-Alonso, J. (2022). A reliable data-based smoothing parameter selection method for circular kernel estimation.
density.circular
, kern.den.circ, bw.pi
, bw.rt
, bw.CV
, bw.boot
set.seed(2022) n <- 50 x <- rcircmix(n,model=6) # Concentration parameter for density estimation bw.AA(x) # Solve-the-equation concentration parameter bw.AA(x, method="dpi") # Direct plug-in concentration parameter # Concentration parameter for the density derivative estimate bw.AA(x, method="ste") # Solve-the-equation concentration parameter bw.AA(x, deriv.order=1, method="dpi") # Direct plug-in concentration parameter
Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.