心灵 发表于 2014-6-29 16:03:41

自助法示例

n <- 1000 #样本数据集数量
B <- 1000 # boot.samples
alpha <- 0.05 #置信概率
df <- 6
true.mu <- 0 # 真是均值
true.sd <- 1 # 真实标准差

# 模拟数据生成
x <- rnorm(n,mean = true.mu, sd = true.sd)

sample.mean.x <- mean(x) #样本均值
sample.sd.x <- sd(x) #样本标准差
sample.se.x <- sample.sd.x/sqrt(n) #样本标准误
sample.conf.x <- sample.mean.x + c(-1,1)*qnorm(alpha/2,lower.tail=F)*sample.se.x #样本95%置信区间

# 为自助法预留缓存向量
boot.x <- vector(mode="numeric",length=B)
boot.mean <- vector(mode="numeric",length=B)
boot.sd <- vector(mode="numeric",length=B)
boot.t <- vector(mode="numeric",length=B)

for(i in 1:B)
{
boot.x <- sample(x, size=n, replace=T)
boot.mean <- mean(boot.x)
boot.sd <- sd(boot.x)
boot.t <- (sample.mean.x-boot.mean)/(boot.sd/sqrt(n))
}

# bootstrap 统计量
boot.mean.x <- mean(boot.mean)
boot.sd.x <- mean(boot.sd)
boot.se.x <- boot.sd.x/sqrt(B)
boot.t.quantile <- quantile(boot.t,probs = c(alpha/2,1-alpha/2))
boot.mean.quantile <- quantile(boot.mean,probs = c(alpha/2,1-alpha/2))

boot.conf.x <- boot.mean.x + c(-1,1)*qt(alpha/2,df=B-1,lower.tail=F)*boot.se.x
boot.conf.x2 <- boot.mean.x + boot.t.quantile*boot.se.x

true.conf.x <- 2*sample.mean.x - c(boot.mean.quantile,boot.mean.quantile)

#boot.mean.x
#boot.sd.x
#boot.se.x
#boot.conf.x
#boot.conf.x2

#true.conf.x

#sample.mean.x
#sample.sd.x
#sample.se.x
#sample.conf.x


hist(boot.mean, col = "lightblue", border = "pink",freq = F, main="Normal distribution")
lines(density(boot.mean),col="blue", lwd=2)
abline(v=0, col="red",lwd=2)

message("boot.mean.x = ", format(boot.mean.x,digits = 4),"         sample.mean.x = ", format(sample.mean.x,digits = 4),"\n",
      "boot.sd.x = ", format(boot.sd.x,digits = 4),"               sample.sd.x = ", format(sample.sd.x,digits = 4),"\n",
      "boot.conf.x = ", format(boot.conf.x,digits = 4),"      sample.conf.x = ", format(sample.conf.x,digits = 4),"\n",
      "boot.conf.x2 = ", format(boot.conf.x2,digits = 4),"      true.conf.x = ", format(true.conf.x,digits = 4),"\n")

这段代码主要简单得阐述了bootstrap技术，并对比了在bootstrap统计量和样本统计量以及（真实）统计量的差异。

ｙōｙō琴緣 发表于 2014-8-20 08:54:51

:P不错哦 ，么么哒

Freedzhang 发表于 2015-1-24 12:46:13

{:soso_e179:}{:soso_e179:}

txyw 发表于 2015-5-15 13:47:17

bootstrap和蒙特卡洛间的区别大不大？

wjyalx 发表于 2016-3-17 21:22:13

这个的确不错啊，把统计学知识和机器学习结合起来，值得学习哈。:lol

suppppperrr 发表于 2017-11-21 00:42:59

您好~~~这个用于对比的truemean应该是sample的mean还是总体population的mean呀？用不用先rnorm一个总体，在从总体里抽样出来作为样本（sample）?正在做一项相关的作业，这里感到很困惑。
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