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fun_ahrypt <- function(oy, od, oz, best, tau, alpha, ...) {
n <- length(oy)
oyl <- c(0, oy[1:(n - 1)])
oyr <- c(oy[2:n], tau)
bt <- exp(-best)
bt1 <- bt[1]
bt2 <- bt[2]
jh <- 1e-08
K <- n:1
b <- as.numeric(best) + cbind(c(jh, 0), -c(jh, 0), c(0, jh), -c(0,
jh))
gamma1 <- exp(-matrix(b[1, ], nrow = 1) %x% oz)
gamma2 <- exp(-matrix(b[2, ], nrow = 1) %x% oz)
Lambda1 <- apply(od * gamma1/K, 2, cumsum)
Lambda2 <- apply(od * gamma2/K, 2, cumsum)
P <- exp(-Lambda2)
PL <- rbind(1, P[1:(n - 1), ])
R <- apply(PL * od * gamma1/K, 2, cumsum)/P
denom <- gamma1 + gamma2 * R
u1 <- -(oz * od) %*% (gamma1/denom) + oz %*% (R/denom)
u2 <- -(oz * od) %*% (gamma2 * R/denom) + oz %*% (log(denom/gamma1)/gamma2) -
oz %*% (R/denom)
qf <- rbind(u1, u2)
pq <- cbind(qf[, 1] - qf[, 2], qf[, 3] - qf[, 4])/2/jh
pr <- cbind(R[, 1] - R[, 2], R[, 3] - R[, 4])/2/jh
r <- R[, 1]
rl <- c(0, r[1:(n - 1)])
dr <- r - rl
po <- P[, 1]
plo <- PL[, 1]
g1 <- gamma1[, 1]
g2 <- gamma2[, 1]
den <- bt1 + bt2 * r
denl <- bt1 + bt2 * rl
hr <- (1 + r)/den
ntl <- sum(oy < tau)
avv <- as.numeric(t(c(1/bt1, hr[1:ntl])) %*% c(c(oy[1:ntl], tau) -
c(0, oy[1:ntl]))/tau)
tem <- (bt1 - bt2)/den^2
tem0 <- (bt1 - bt2)/bt1^2
a <- cbind(tem * pr[, 1] + bt1 * (1 + r)/den^2, tem * pr[, 2] + bt2 *
r * (1 + r)/den^2)
a0 <- c(1/bt1, 0)
cua <- oy[1] * a0 + t(c(oy[2:ntl], tau) - oy[1:ntl]) %*% a[1:ntl,
]
br <- tem/po
br0 <- tem0
tem1 <- c(br0, br[1:(n - 1)]) * (oy - oyl)
cb <- oy[1] * br0 + sum((c(oy[2:ntl], tau) - oy[1:ntl]) * br[1:ntl]) -
cumsum(tem1) + tem1
cb <- cb * (oy <= tau)
inrs1 <- c()
inrs2 <- c()
inrw <- c()
inrsw1 <- c()
inrsw2 <- c()
for (ti in 1:n) {
yk <- (oy >= oy[ti])
dk <- g1 + r[ti] * g2
tek <- yk/dk
inrs1[ti] <- t(oz) %*% (g1 * tek/dk)
inrs2[ti] <- R[ti] * t(oz) %*% (g2 * tek/dk)
inrw[ti] <- t(g2) %*% tek
inrsw1[ti] <- t(oz) %*% (g1 * g2 * tek/dk^2)
inrsw2[ti] <- R[ti] * t(oz) %*% (g2^2 * tek/dk^2)
}
inr1 <- (inrsw1 - inrw * inrs1/K) * dr/po
inr2 <- (inrsw2 - inrw * inrs2/K) * dr/po
inr1 <- inr1 + sum(inr1) - cumsum(inr1)
inr2 <- inr2 + sum(inr2) - cumsum(inr2)
rmul <- plo/K
inr1 <- inr1 * rmul
inr2 <- inr2 * rmul
inq <- solve(-pq/n)
ff <- cbind(bt1/den, bt2 * r/den)
k1all <- cumsum(1 - oz[n:1])[n:1]
k2all <- cumsum(oz[n:1])[n:1]
x1 <- cbind(-k2all/K * ff[, 1] * hr + inr1 * (1 + r), -k2all/K * ff[,
2] * hr + inr2 * (1 + r))
xn <- cbind(k1all/K * ff[, 1] + inr1 * den, k1all/K * ff[, 2] + inr2 *
den)
nu1 <- rmul * (1 + r)
nun <- rmul * den
d11 <- k1all * dr/(1 + r)
dnn <- k2all * dr/den
sig1 <- cua %*% inq %*% (t(x1) %*% (d11 %x% matrix(c(1, 1), nrow = 1) *
x1) + t(xn) %*% (dnn %x% matrix(c(1, 1), nrow = 1) * xn)) %*%
t(inq)
sig1 <- sig1 %*% t(cua)/n
sig2 <- n * (t((nu1 * cb)^2) %*% d11 + t((nun * cb)^2) %*% dnn)
sig12 <- colSums((d11 * nu1 * cb) %x% matrix(c(1, 1), nrow = 1) *
x1 + ((dnn * nun * cb) %x% matrix(c(1, 1), nrow = 1)) * xn)
sig12 <- sig12 %*% t(cua %*% inq)
sig <- sig1 + sig2 + 2 * sig12
stmb <- sqrt(sig)
ca3 <- qnorm(1 - alpha/2)
uppc <- exp(ca3 * stmb/sqrt(n)/tau/avv) * avv
lowc <- exp(-ca3 * stmb/sqrt(n)/tau/avv) * avv
zv <- sqrt(n) * log(avv) * avv * tau/stmb
result <- list()
result$estimate <- avv
result$lower <- as.numeric(lowc)
result$upper <- as.numeric(uppc)
result$z <- as.numeric(zv)
result$pvalue <- 2 * (1 - pnorm(abs(zv)))
return(result)
}
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