naive: The Chernoff or 'naive' mode estimator

In modeest: Mode Estimation

The Chernoff or 'naive' mode estimator

Description

This estimator, also called the naive mode estimator, is defined as the center of the interval of given length containing the most observations. It is identical to Parzen's kernel mode estimator, when the kernel is chosen to be the uniform kernel.

Usage

naive(x, bw = 0.5)

Arguments

x	numeric. Vector of observations.
bw	numeric. The smoothing bandwidth to be used. Should belong to (0, 1). See below.

Value

A numeric vector is returned, the mode estimate, which is the center of the interval of length 2*bw containing the most observations.

Note

The user may call naive through mlv(x, method = "naive", bw).

References

• Chernoff H. (1964). Estimation of the mode. Ann. Inst. Statist. Math., 16:31-41.

• Leclerc J. (1997). Comportement limite fort de deux estimateurs du mode : le shorth et l'estimateur naif. C. R. Acad. Sci. Paris, Serie I, 325(11):1207-1210.

See Also

mlv for general mode estimation; parzen for Parzen's kernel mode estimation.

Examples

# Unimodal distribution
x <- rf(10000, df1 = 40, df2 = 30)

## True mode
fMode(df1 = 40, df2 = 30)

## Estimate of the mode
mean(naive(x, bw = 1/4))
mlv(x, method = "naive", bw = 1/4)

modeest documentation built on Sept. 21, 2026, 1:06 a.m.