Bandwidth estimation for CVE.
If no bandwidth or function for calculating it is supplied, the CVE method defaults to using the following formula (version 1)
h = (2 * tr(Σ) / p) * (1.2 * n^(-1 / (4 + k)))^2
Alternative version 2 is used for dimension prediction which is given by
h = (2 * tr(Σ) / p) * χ_k^-1((nObs - 1) / (n - 1))
with n the sample size, p the dimension of X and Σ is (n - 1) / n times the sample covariance matrix of X.
estimate.bandwidth(X, k, nObs, version = 1L)
X |
the n x p matrix of predictor values. |
k |
the SDR dimension. |
nObs |
number of points in a slice, only for version 2. |
version |
either |
Estimated bandwidth h.
# set dimensions for simulation model p <- 5; k <- 1 # create B for simulation B <- rep(1, p) / sqrt(p) # samplsize n <- 100 set.seed(21) #creat predictor data x ~ N(0, I_p) x <- matrix(rnorm(n * p), n, p) # simulate response variable # y = f(B'x) + err # with f(x1) = x1 and err ~ N(0, 0.25^2) y <- x %*% B + 0.25 * rnorm(100) # calculate cve with method 'simple' for k = 1 set.seed(21) cve.obj.simple <- cve(y ~ x, k = k) print(estimate.bandwidth(x, k = k))
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