tsybakov: The Tsybakov mode estimator
In modeest: Mode Estimation

Description Usage Arguments Details Value Warning Note References See Also Examples

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

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

`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` for more details on some of these kernels.
`dmp`	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)`.

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

A numeric value is returned, the mode estimate.

The Tsybakov mode estimate as it is presently computed does not work very well. The reasons of this inefficiency should be further investigated.

The user may call tsybakov through mlv(x, method = "tsybakov", ...).

Mizoguchi R. and Shimura M. (1976). Nonparametric Learning Without a Teacher Based on Mode Estimation. IEEE Transactions on Computers, C25(11):1109-1117.
Tsybakov A. (1990). Recursive estimation of the mode of a multivariate distribution. Probl. Inf. Transm., 26:31-37.
Djeddour K., Mokkadem A. et Pelletier M. (2003). Sur l'estimation recursive du mode et de la valeur modale d'une densite de probabilite. Technical report 105.
Djeddour K., Mokkadem A. et Pelletier M. (2003). Application du principe de moyennisation a l'estimation recursive du mode et de la valeur modale d'une densite de probabilite. Technical report 106.

mlv for general mode estimation.

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)
mlv(x, method = "tsybakov", kernel = "gaussian", alpha = 0.99)