28 lines
1.0 KiB
R
28 lines
1.0 KiB
R
#' Estimated bandwidth for CVE.
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#'
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#' Estimates a propper bandwidth \code{h} according
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#' \deqn{%
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#' h = \chi_{p-q}^{-1}\left(\frac{nObs - 1}{n-1}\right)\frac{2 tr(\Sigma)}{p}}{%
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#' h = qchisq( (nObs - 1)/(n - 1), p - q ) 2 tr(Sigma) / p}
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#'
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#' @param X data matrix of dimension (n x p) with n data points X_i of dimension
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#' q. Therefor each row represents a datapoint of dimension p.
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#' @param k Guess for rank(B).
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#' @param nObs Ether numeric of a function. If specified as numeric value
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#' its used in the computation of the bandwidth directly. If its a function
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#' `nObs` is evaluated as \code{nObs(nrow(x))}. The default behaviou if not
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#' supplied at all is to use \code{nObs <- nrow(x)^0.5}.
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#'
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#' @seealso [\code{\link{qchisq}}]
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#' @export
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estimate.bandwidth <- function(X, k, nObs) {
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n <- nrow(X)
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p <- ncol(X)
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X_centered <- scale(X, center=TRUE, scale=FALSE)
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Sigma <- (1 / n) * t(X_centered) %*% X_centered
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quantil <- qchisq((nObs - 1) / (n - 1), k)
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return(2 * quantil * sum(diag(Sigma)) / p)
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}
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