Extracts estimated SDR basis.
Returns the SDR basis matrix for dimension k
, i.e. returns the
cve-estimate of B with dimension p x k.
## S3 method for class 'cve' coef(object, k, ...)
The matrix B of dimensions p x k.
# set dimensions for simulation model p <- 8 # sample dimension k <- 2 # real dimension of SDR subspace n <- 100 # samplesize # create B for simulation b1 <- rep(1 / sqrt(p), p) b2 <- (-1)^seq(1, p) / sqrt(p) B <- cbind(b1, b2) 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, x2) = x1^2 + 2 * x2 and err ~ N(0, 0.1^2) y <- (x %*% b1)^2 + 2 * (x %*% b2) + 0.1 * rnorm(100) # calculate cve for k = 2, 3 cve.obj <- cve(y ~ x, min.dim = 2, max.dim = 3) # get cve-estimate for B with dimensions (p, k = 2) B2 <- coef(cve.obj, k = 2) # Projection matrix on span(B) # equivalent to `B %*% t(B)` since B is semi-orthonormal PB <- B %*% solve(t(B) %*% B) %*% t(B) # Projection matrix on span(B2) # equivalent to `B2 %*% t(B2)` since B2 is semi-orthonormal PB2 <- B2 %*% solve(t(B2) %*% B2) %*% t(B2) # compare estimation accuracy by Frobenius norm of difference of projections norm(PB - PB2, type = 'F')
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