modeest (version 1.06)

venter: Venter / Dalenius / LMS Mode Estimator

Description

This function computes Venter mode estimator, also called 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.

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. The user should either give the bandwidth bw or the argument k, k being taken equal to ceiling(bw*ny) - 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 $L_{-\infty}$ 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. % %\item Rousseeuw and Leroy, 1987 #(ou bien Andrews ?)
• Leclerc J. (1997). Comportement limite fort de deux estimateurs du mode : le shorth et l'estimateur na�f.C. R. Acad. Sci. Paris, S�rie I,325(11):1207-1210.
• Leclerc J. (2000). Strong limiting behavior of two estimates of the mode: the shorth and the naive estimator.Statistics and Decisions,18(4). % %\item Bickel ??

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))