R: The Venter / Dalenius / LMS Mode Estimator

venter {modeest} | R Documentation

## The Venter / Dalenius / LMS Mode Estimator

### Description

This function computes the Venter mode estimator, also called the Dalenius, or LMS (Least Median Square) mode estimator.

### Usage

      venter(x,
             bw = NULL,
             k,
             iter = 1,
             type = 1,
             tie.action = "mean",
             tie.limit = 0.05)

      shorth(x,
             ...)

### Arguments

`x` | numeric. Vector of observations.
`bw` | numeric. The bandwidth to be used. Should belong to (0, 1]. See 'Details'.
`k` | numeric. See 'Details'.
`iter` | numeric. Number of iterations.
`type` | numeric or character. The type of Venter estimate to be computed. 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.
`...` | Further arguments.

### Details

The modal interval, i.e. the shortest interval among intervals containing `k+1` observations, is first computed. The user should either give the bandwidth `bw` or the argument `k`, `k` being taken equal to `ceiling(bw*n) - 1` if missing.
If `type = 1`, the midpoint of the modal interval is returned. If `type = 2`, the `floor((k+1)/2)`th element of the modal interval is returned. If `type = 3` or `type = "dalenius"`, the median of the modal interval is returned. If `type = 4` or `type = "shorth"`, the mean of the modal interval is returned. If `type = 5` or `type = "ekblom"`, Ekblom's L_{-infinity} estimate is returned, see Ekblom (1972). If `type = 6` or `type = "hsm"`, the half sample mode (hsm) is computed, see `hsm`.

### Value

A numeric value is returned, the mode estimate.

### Note

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

### Author(s)

P. Poncet

### References

- Dalenius T. (1965). The Mode - A Negleted Statistical Parameter. J. Royal Statist. Soc. A, 128:110-117.

- Venter J.H. (1967). On estimation of the mode. Ann. Math. Statist., 38(5):1446-1455.

- Ekblom H. (1972). A Monte Carlo investigation of mode estimators in small samples. Applied Statistics, 21:177-184.

- 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, `hsm` for the half sample mode

### Examples

    library(evd)

    # Unimodal distribution
    x <- rgev(1000, loc = 23, scale = 1.5, shape = 0)

    ## True mode
    gevMode(loc = 23, scale = 1.5, shape = 0)

    ## Estimate of the mode
    venter(x, bw = 1/3)
    M <- mlv(x, method = "venter", bw = 1/3)
    print(M)
    plot(M, xlim = c(20, 30))

[Package modeest version 2.1 Index]