Nothing
weighted.xenv <- function(X, Y, bstrpNum = 0, min.u = 1, max.u = ncol(as.matrix(X)), boot.resi = "full") {
bstrpNum <- ceiling(bstrpNum)
if (bstrpNum < 0) stop("The number of bootstrap samples should be a positive integer.")
if (min.u < 0) stop("The smallest dimension of the envelope subspace is 0.")
if (max.u > ncol(X)) stop("The largest dimension of the envelope subspace is p.")
X <- as.matrix(X)
Y <- as.matrix(Y)
bootse <- NULL
ratios <- NULL
bic_select <- NULL
a <- dim(Y)
n <- a[1]
r <- a[2]
p <- ncol(X)
w.xenv <- function(X, Y, min.u, max.u) {
min.u <- ceiling(min.u)
max.u <- ceiling(max.u)
betaarray <- array(0, c(p, r, max.u-min.u+1))
muarray <- matrix(0, r, max.u-min.u+1)
SigmaXarray <- array(0, c(p, p, max.u-min.u+1))
SigmaYcXarray <- array(0, c(r, r, max.u-min.u+1))
bic.seq <- rep(0, max.u-min.u+1)
w <- rep(0, max.u-min.u+1)
beta <- matrix(0, p, r)
mu <- matrix(0, r, 1)
SigmaX <- matrix(0, p, p)
SigmaYcX <- matrix(0, r, r)
for (i in min.u:max.u) {
m <- xenv(X, Y, i, asy = F)
betaarray[ , , i-min.u+1] <- m$beta
muarray[, i-min.u+1] <- m$mu
SigmaXarray[ , , i-min.u+1] <- m$SigmaX
SigmaYcXarray[ , , i-min.u+1] <- m$SigmaYcX
bic.seq[i-min.u+1] <- -2 * m$loglik + log(n) * (r + r * (r + 1) / 2 + p * (p + 1) / 2 + r * i)
}
for (i in min.u:max.u) {
w[i-min.u+1] <- 1 / sum(exp(bic.seq[i-min.u+1] - bic.seq))
beta <- w[i-min.u+1] * betaarray[ , , i-min.u+1] + beta
mu <- w[i-min.u+1] * muarray[ , i-min.u+1] + mu
SigmaX <- w[i-min.u+1] * SigmaXarray[ , , i-min.u+1] + SigmaX
SigmaYcX <- w[i-min.u+1] * SigmaYcXarray[ , , i-min.u+1] + SigmaYcX
}
return(list(beta = beta, mu = mu, w = w, SigmaX = SigmaX, SigmaYcX = SigmaYcX))
}
m <- w.xenv(X, Y, min.u, max.u)
beta <- m$beta
mu <- m$mu
SigmaX <- m$SigmaX
SigmaYcX <- m$SigmaYcX
w <- m$w
Yfit <- matrix(1, n, 1) %*% t(mu) + X %*% beta
if (boot.resi == "weighted") {
res <- Y - Yfit
} else {
m2 <- xenv(X, Y, p, asy = F)
beta.full <- m2$beta
mu.full <- m2$mu
res <- Y - matrix(1, n, 1) %*% t(mu.full) - X %*% beta.full
}
res1 <- as.matrix(res)
tmp <- res1 %*% chol2inv(chol(SigmaYcX))
resX <- scale(X, center = T, scale = F)
tmpX <- resX %*% chol2inv(chol(SigmaX))
loglik <- - n * (r + p) / 2 * log(2 * pi) - n / 2 * sum(log(eigen(SigmaYcX)$values)) - 1 / 2 * sum(c(tmp) * c(res1)) - n / 2 * sum(log(eigen(SigmaX)$values)) - 1 / 2 * sum(c(tmpX) * c(resX))
if (bstrpNum > 0) {
bootenv <- function(i) {
res.boot <- res[sample(1:n, n, replace = T), ]
Y.boot <- Yfit + res.boot
return(c(w.xenv(X, Y.boot, min.u, max.u)$beta, w.xenv(X, Y.boot, min.u, max.u)$w))
}
bootres <- lapply(1:bstrpNum, function(i) bootenv(i))
bootres <- matrix(unlist(bootres), nrow = bstrpNum, byrow = TRUE)
bootse <- matrix(apply(bootres[, 1:(p*r)], 2, stats::sd), nrow = p)
bic_select <- table(apply(as.matrix(bootres[, (r*p+1):(r*p+max.u-min.u+1)]), 1, which.max))
names(bic_select) <- as.character(strtoi(names(bic_select)) + min.u - 1)
bootse.full <- boot.xenv(X, Y, p, bstrpNum)
ratios <- bootse.full / bootse
}
return(list(beta = beta, mu = mu, SigmaX = SigmaX, SigmaYcX = SigmaYcX, w = w, loglik = loglik, n = n, bootse = bootse, ratios = ratios, bic_select = bic_select))
}
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