modeest (version 2.4.0)

venter: 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,
  warn = FALSE
)
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.

warn

logical. If TRUE, a warning is thrown when a tie is encountered.

...

Further arguments.

Value

A numeric value is returned, the mode estimate.

Details

The modal interval, i.e. the shortest interval among intervals containing k+1 observations, is first computed. (In dimension > 1, this question is known as a 'k-enclosing problem'.) The user should either give the bandwidth bw or the argument k, k being taken equal to ceiling(bw*n) - 1 if missing, so bw can be seen as the fraction of the observations to be considered for the shortest interval.

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 \(L_{-\infty}\) estimate is returned, see Ekblom (1972). If type = 6 or type = "hsm", the half sample mode (hsm) is computed, see hsm.

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

# NOT RUN {
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)
mlv(x, method = "venter", bw = 1/3)

# }