hsm: Half sample mode estimator

In modeest: Mode Estimation

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)

modeest documentation built on Nov. 18, 2019, 5:07 p.m.