R: The Chernoff Mode Estimator

naive {modeest} | R Documentation

## 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.

### Note

The user should preferentially call `naive` through `mlv(x, method = "naive", bw)`. This returns an object of class `mlv`.

### Author(s)

P. Poncet

### 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))
    M <- mlv(x, method = "naive", bw = 1/4)
    print(M)
    plot(M, xlim = c(0,2))

[Package modeest version 2.1 Index]