sigma2.hat<-(n-1)*var(x)/n #bootstrap estimate of bias B <-2000 #larger for estimating bias sigma2.b <numeric(B) for (b in 1:B){ i <sample(1:n,size n,replace TRUE) sigma2.b[b]<-(n-1)*var(x[i])/n bias <mean(sigma2.b sigma2.hat) bias Code 在这种情形下，2过低的估计了参数a2. 例6比值参数估计的偏差的Bootstrap估计.以包bootstrap里的patch数 据为例.该数据是测量了8个人使用3种不同的药物后血液中某种荷尔蒙的含 量.这三种药物分别是安慰剂，旧药品（经过FDA审批的），新药品（某个新工厂 相同的工艺下生产的，按FDA规定，新工厂生产的药品也要审批).研究的目的 是比较新药和旧药的等价性.如果可以证明新药和旧药之间的等价性，则对新 Previous Next First Last Back Forward 14
sigma2.hat<-(n-1)*var(x)/n #bootstrap estimate of bias B <- 2000 #larger for estimating bias sigma2.b <- numeric(B) for (b in 1:B) { i <- sample(1:n, size = n, replace = TRUE) sigma2.b[b] <-(n-1)*var(x[i])/n } bias <- mean(sigma2.b - sigma2.hat) bias ↓Code 3˘´ú/e, ˆσ 2L$O ÎÍσ 2 . ~6 'äÎÍO† BootstrapO. ±ùbootstrapppatchÍ ‚è~. TÍ‚¥ˇ˛ 8á<¶^3´ÿ”Ü‘…ó•,´÷ѹ ˛. ˘n´Ü‘©O¥S§J, ŒÜ¨(²LFDA"1), #ܨ(,á#ÛÇ É”Û²e), UFDA5½, #ÛÇ)ܨèá"1). Ôƒ8 ¥'#Ü⁄ŒÜ d5. XJå±y²#Ü⁄ŒÜÉm d5, KÈ# Previous Next First Last Back Forward 14
药就不需要完全重新向FDA申请审批了.等价性的标准是对比值参数 E(new)-E(old) 0= E(old)-E(placebo) 若≤0.20，则新药和旧药就等价.估计9的统计量为卫/Z.这两个变量 在patch数据中给出.我们的目标是计算此估计偏差的Bootstrap估计 Code data(patch,package ="bootstrap") patch n<-nrow(patch)#in bootstrap package B<-2000 theta.b <-numeric(B) theta.hat <-mean(patch$y)/mean(patch$z) #bootstrap for (b in 1:B){ i<-sample(1:n,size n,replace TRUE) y <-patchSy[i] z <patch$z[i] theta.b[b]<-mean(y)/mean(z) y Previous Next First Last Back Forward 15
Ü“ÿIá #ïFDAû"1 . d5IO¥È'äÎÍ θ = E(new) − E(old) E(old) − E(placebo) . e|θ| ≤ 0.20, K#Ü⁄ŒÜ“ d. Oθ⁄O˛èY /¯ Z¯. ˘¸áC˛ 3patchÍ‚•â—. ·Ç8I¥OédO† BootstrapO. ↑Code data(patch, package = "bootstrap") patch n <- nrow(patch) #in bootstrap package B <- 2000 theta.b <- numeric(B) theta.hat <- mean(patch$y) / mean(patch$z) #bootstrap for (b in 1:B) { i <- sample(1:n, size = n, replace = TRUE) y <- patch$y[i] z <- patch$z[i] theta.b[b] <- mean(y) / mean(z) } Previous Next First Last Back Forward 15