46 lines
1.4 KiB
R
46 lines
1.4 KiB
R
#' Bandwidth estimation for CVE.
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#'
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#' Estimates a bandwidth \code{h} according
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#' \deqn{%
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#' h = (2 * tr(\Sigma) / p) * (1.2 * n^{-1 / (4 + k)})^2}{%
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#' h = (2 * tr(\Sigma) / p) * (1.2 * n^(\frac{-1}{4 + k}))^2}
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#' with \eqn{n} the sample size, \eqn{p} its dimension
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#' (\code{n <- nrow(X); p <- ncol(X)}) and the covariance-matrix \eqn{\Sigma}
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#' which is \code{(n-1)/n} times the sample covariance estimate.
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#'
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#' @param X data matrix with samples in its rows.
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#' @param k Dimension of lower dimensional projection.
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#' @param nObs number of points in a slice, see \eqn{nObs} in CVE paper.
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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(cve.obj.simple$res$'1'$h)
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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) {
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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 <- 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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}
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