modeest (version 2.1)

naive: The Chernoff 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 = 1/2)

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.

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

# NOT RUN {
# 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))
M <- mlv(x, method = "naive", bw = 1/4)
print(M)
plot(M, xlim = c(0,2))
# }