| grenander {modeest} | R Documentation |
The Grenander mode estimator
Description
This function computes the Grenander mode estimator.
Usage
grenander(x, bw = NULL, k, p, ...)
Arguments
x |
numeric. Vector of observations. |
bw |
numeric. The bandwidth to be used. Should belong to (0, 1]. |
k |
numeric. Paramater 'k' in Grenander's mode estimate, see below. |
p |
numeric. Paramater 'p' in Grenander's mode estimate, see below.
If |
... |
Additional arguments to be passed to |
Details
The Grenander estimate is defined by
\frac{ \sum_{j=1}^{n-k} \frac{(x_{j+k} + x_{j})}{2(x_{j+k} - x_{j})^p} }
{ \sum_{j=1}^{n-k} \frac{1}{(x_{j+k} - x_{j})^p} }
If p tends to infinity, this estimate tends to the Venter mode estimate;
this justifies to call venter if p = Inf.
The user should either give the bandwidth bw or the argument k,
k being taken equal to ceiling(bw*n) - 1 if missing.
Value
A numeric value is returned, the mode estimate.
If p = Inf, the venter mode estimator is returned.
Note
The user may call grenander through
mlv(x, method = "grenander", bw, k, p, ...).
Author(s)
D.R. Bickel for the original code, P. Poncet for the slight modifications introduced.
References
Grenander U. (1965). Some direct estimates of the mode. Ann. Math. Statist., 36:131-138.
Dalenius T. (1965). The Mode - A Negleted Statistical Parameter. J. Royal Statist. Soc. A, 128:110-117.
Adriano K.N., Gentle J.E. and Sposito V.A. (1977). On the asymptotic bias of Grenander's mode estimator. Commun. Statist.-Theor. Meth. A, 6:773-776.
Hall P. (1982). Asymptotic Theory of Grenander's Mode Estimator. Z. Wahrsch. Verw. Gebiete, 60:315-334.
See Also
mlv for general mode estimation;
venter for the Venter mode estimate.
Examples
# Unimodal distribution
x <- rnorm(1000, mean = 23, sd = 0.5)
## True mode
normMode(mean = 23, sd = 0.5) # (!)
## Parameter 'k'
k <- 5
## Many values of parameter 'p'
ps <- seq(0.1, 4, 0.01)
## Estimate of the mode with these parameters
M <- sapply(ps, function(p) grenander(x, p = p, k = k))
## Distribution obtained
plot(density(M), xlim = c(22.5, 23.5))