| grenander {modeest} | R Documentation |
This function computes the Grenander mode estimator.
grenander(x,
bw = NULL,
k,
p,
...)
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. |
p |
numeric. Paramater 'p' in Grenander's mode estimate.
If |
... |
further arguments to be passed to |
The Grenander estimate is defined by
( sum_{j=1}^{n-k} (x_{j+k} + x_{j})/(2(x_{j+k} - x_{j})^p) ) / ( sum_{j=1}^{n-k} 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.
A numeric value is returned, the mode estimate.
If p = Inf, the Venter mode estimator is returned.
The user should preferentially call grenander through
mlv(x, method = "grenander", bw, k, p, ...).
This returns an object of class mlv.
D.R. Bickel for the original code,
P. Poncet for the slight modifications introduced.
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.
mlv for general mode estimation;
venter for the Venter mode estimate
# 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' p <- seq(0.1, 4, 0.01) ## Estimate of the mode with these parameters M <- sapply(p, function(pp) grenander(x, p = pp, k = k)) ## Distribution obtained plot(density(M), xlim = c(22.5, 23.5))