56 lines
2.0 KiB
R
56 lines
2.0 KiB
R
#' Bandwidth estimation for CVE.
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#'
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#' If no bandwidth or function for calculating it is supplied, the CVE method
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#' defaults to using the following formula (version 1)
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#' \deqn{%
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#' h = \frac{2 tr(\Sigma)}{p} (1.2 n^{\frac{-1}{4 + k}})^2}{%
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#' h = (2 * tr(\Sigma) / p) * (1.2 * n^(-1 / (4 + k)))^2}
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#' Alternative version 2 is used for dimension prediction which is given by
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#' \deqn{%
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#' h = \frac{2 tr(\Sigma)}{p} \chi_k^{-1}(\frac{nObs - 1}{n - 1})}{%
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#' h = (2 * tr(\Sigma) / p) * \chi_k^-1((nObs - 1) / (n - 1))}
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#' with \eqn{n} the sample size, \eqn{p} the dimension of \eqn{X} and
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#' \eqn{\Sigma} is \eqn{(n - 1) / n} times the sample covariance matrix of
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#' \eqn{X}.
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#'
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#' @param X the \eqn{n\times p}{n x p} matrix of predictor values.
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#' @param k the SDR dimension.
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#' @param nObs number of points in a slice, only for version 2.
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#' @param version either \code{1} or \code{2}.
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#'
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#' @return Estimated bandwidth \code{h}.
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#'
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#' @examples
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#' # set dimensions for simulation model
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#' p <- 5; k <- 1
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#' # create B for simulation
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#' B <- rep(1, p) / sqrt(p)
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#' # samplsize
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#' n <- 100
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#' set.seed(21)
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#' #creat predictor data x ~ N(0, I_p)
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#' x <- matrix(rnorm(n * p), n, p)
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#' # simulate response variable
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#' # y = f(B'x) + err
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#' # with f(x1) = x1 and err ~ N(0, 0.25^2)
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#' y <- x %*% B + 0.25 * rnorm(100)
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#' # calculate cve with method 'simple' for k = 1
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#' set.seed(21)
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#' cve.obj.simple <- cve(y ~ x, k = k)
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#' print(estimate.bandwidth(x, k = k))
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#' @export
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estimate.bandwidth <- function (X, k, nObs, version = 1L) {
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n <- nrow(X)
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p <- ncol(X)
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if (version == 1) {
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X_centered <- scale(X, center = TRUE, scale = FALSE)
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Sigma <- crossprod(X_centered, X_centered)/n
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return((2 * sum(diag(Sigma))/p) * (1.2 * n^(-1/(4 + k)))^2)
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} else if (version == 2) {
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X_c <- scale(X, center = TRUE, scale = FALSE)
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return(2 * qchisq((nObs - 1) / (n - 1), k) * sum(X_c^2) / (n * p))
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} else {
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stop("Unknown version.")
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}
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}
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