| hsm {modeest} | R Documentation |
Half sample mode estimator
Description
This function computes the Robertson-Cryer mode estimator
described in Robertson and Cryer (1974),
also called half sample mode (if bw = 1/2)
or fraction sample mode (for some other bw) by Bickel (2006).
Usage
hsm(x, bw = NULL, k, tie.action = "mean", tie.limit = 0.05, ...)
Arguments
x |
numeric. Vector of observations. |
bw |
numeric or function. The bandwidth to be used. Should belong to (0, 1]. |
k |
numeric. See 'Details'. |
tie.action |
character. The action to take if a tie is encountered. |
tie.limit |
numeric. A limit deciding whether or not a warning is given when a tie is encountered. |
... |
Additional arguments. |
Details
The modal interval, i.e. the shortest interval among
intervals containing k+1 observations, is computed
iteratively, until only one value is found, the mode estimate.
At each step i, one takes k = ceiling(bw*n) - 1,
where n is the length of the modal interval computed
at step i-1.
If bw is of class "function",
then k = ceiling(bw(n)) - 1 instead.
Value
A numeric value is returned, the mode estimate.
Note
The user may call hsm through
mlv(x, method = "hsm", ...).
Author(s)
D.R. Bickel for the original code, P. Poncet for the slight modifications introduced.
References
Robertson T. and Cryer J.D. (1974). An iterative procedure for estimating the mode. J. Amer. Statist. Assoc., 69(348):1012-1016.
Bickel D.R. and Fruehwirth R. (2006). On a Fast, Robust Estimator of the Mode: Comparisons to Other Robust Estimators with Applications. Computational Statistics and Data Analysis, 50(12):3500-3530.
See Also
mlv for general mode estimation;
venter for the Venter mode estimate.
Examples
# Unimodal distribution
x <- rweibull(10000, shape = 3, scale = 0.9)
## True mode
weibullMode(shape = 3, scale = 0.9)
## Estimate of the mode
bandwidth <- function(n, alpha) {1/n^alpha}
hsm(x, bw = bandwidth, alpha = 2)
mlv(x, method = "hsm", bw = bandwidth, alpha = 2)