54 lines
1.6 KiB
R
54 lines
1.6 KiB
R
% Generated by roxygen2: do not edit by hand
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% Please edit documentation in R/estimateBandwidth.R
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\name{estimate.bandwidth}
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\alias{estimate.bandwidth}
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\title{Bandwidth estimation for CVE.}
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\usage{
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estimate.bandwidth(X, k, nObs, version = 1L)
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}
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\arguments{
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\item{X}{the \eqn{n\times p}{n x p} matrix of predictor values.}
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\item{k}{the SDR dimension.}
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\item{nObs}{number of points in a slice, only for version 2.}
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\item{version}{either \code{1} or \code{2}.}
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}
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\value{
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Estimated bandwidth \code{h}.
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}
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\description{
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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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\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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}
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