tsybakov {modeest}R Documentation

Tsybakov Mode Estimator

Description

This mode estimator is based on a gradient-like recursive algorithm. It includes Mizoguchi-Shimura (1976) mode estimator, based on the window training procedure.

Usage

tsybakov(x, 
         bw = NULL, 
         a, 
         alpha = 0.9, 
         kernel = "triangular", 
         djeddour = TRUE, 
         par = shorth(x))

Arguments

x numeric. Vector of observations.
bw numeric. Vector of length length(x) giving the sequence of smoothing bandwidths to be used.
a numeric. Vector of length length(x) used in the gradient algorithm.
alpha numeric. An alternative way of specifying a. See 'Details'.
kernel character. The kernel to be used. Available kernels are "biweight", "cosine", "eddy", "epanechnikov", "gaussian", "optcosine", "rectangular", "triangular", "uniform". See density.default for more details on some of these kernels.
djeddour logical. If TRUE, Djeddour et al. version of the estimate is used.
par numeric. Initial value in the gradient algorithm. Default value is shorth(x).

Details

If bw is missing, then bw = (1:length(x))^(-1/7), which is the default value advised by Djeddour et al (2003). If a is missing, then a = (1:length(x))^(-alpha) (with alpha = 0.9 is alpha is missing), which is the default value advised by Djeddour et al (2003).

Value

A numeric value is returned, the mode estimate.

Warning

The Tsybakov mode estimate as it is presently computed does not work very well. The reasons of this inefficiency are under investigation.

Note

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

Author(s)

Paul Poncet paulponcet@yahoo.fr

References

See Also

mlv for general mode estimation

Examples

x <- rbeta(1000, shape1 = 2, shape2 = 5)
## True mode:
betaMode(shape1 = 2, shape2 = 5)
## Estimation:
tsybakov(x, kernel = "triangular")
tsybakov(x, kernel = "gaussian", alpha = 0.99)
M <- mlv(x, method = "tsybakov", kernel = "gaussian", alpha = 0.99)
print(M)
plot(M)

[Package modeest version 1.06 Index]