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#' @title
#' The Chernoff or 'naive' mode estimator
#'
#' @description
#' This estimator, also called the *naive* mode estimator, is defined as the
#' center of the interval of given length containing the most observations.
#' It is identical to Parzen's kernel mode estimator, when the kernel is chosen
#' to be the uniform kernel.
#'
#' @note
#' The user may call \code{naive} through
#' \code{mlv(x, method = "naive", bw)}.
#'
#' @references
#' \itemize{
#' \item Chernoff H. (1964).
#' Estimation of the mode.
#' \emph{Ann. Inst. Statist. Math.}, \bold{16}:31-41.
#'
#' \item Leclerc J. (1997).
#' Comportement limite fort de deux estimateurs du mode :
#' le shorth et l'estimateur naif.
#' \emph{C. R. Acad. Sci. Paris, Serie I}, \bold{325}(11):1207-1210.
#' }
#'
#' @param x
#' numeric. Vector of observations.
#'
#' @param bw
#' numeric. The smoothing bandwidth to be used. Should belong to (0, 1). See below.
#'
#' @return
#' A numeric vector is returned, the mode estimate,
#' which is the center of the interval of length \code{2*bw}
#' containing the most observations.
#'
#' @seealso
#' \code{\link[modeest]{mlv}} for general mode estimation;
#' \code{\link[modeest]{parzen}} for Parzen's kernel mode estimation.
#'
#' @export
#' @aliases Chernoff chernoff
# #' @rdname parzen
#'
#' @examples
#' # Unimodal distribution
#' x <- rf(10000, df1 = 40, df2 = 30)
#'
#' ## True mode
#' fMode(df1 = 40, df2 = 30)
#'
#' ## Estimate of the mode
#' mean(naive(x, bw = 1/4))
#' mlv(x, method = "naive", bw = 1/4)
#'
naive <-
function(x,
bw = 1/2)
{
parzen(x = x, bw = bw, kernel = "uniform", abc = TRUE)
}
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