Half sample mode estimator
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).
hsm(x, bw = NULL, k, tie.action = "mean", tie.limit = 0.05, ...)
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. |
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.
A numeric value is returned, the mode estimate.
The user may call hsm through
mlv(x, method = "hsm", ...).
D.R. Bickel for the original code, P. Poncet for the slight modifications introduced.
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.
# 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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.