README.md

In lvli19/StatComp18096: Three functions in statscomp

StatComp18096

Overview

StatComp18096 is a simple R package developed to compute the bias and the standard error of an estimator with resampling methods.Three functions are considered, namely, boot (using bootstrap method) and jack and jackafterboot. For each function, examples are given.

Comparing boot, jack and jackafterboot

The source R code for boot is as follows: ```{r,eval=FALSE} boot <- function(data,func=NULL, B){ theta.hat <- func(data) #set up the bootstrap n <- length(data) #sample size theta.b <- numeric(B) #storage for replicates for (b in 1:B) { #randomly select the indices i <- sample(1:n, size = n, replace = TRUE) dat <- data[i] #i is a vector of indices theta.b[b] <- func(dat) } #bootstrap estimate of standard error of R bias.theta <- mean(theta.b - theta.hat) se <- sd(theta.b) return(list(bias.b = bias.theta,se.b = se)) }

```{r,eval=FALSE}
jack <- function(data,func=NULL){
  theta.hat <- func(data)
  #set up the bootstrap
  #B is the number of replicates
  n <- length(data)      #sample size
  M <- numeric(n)
  for (i in 1:n) { #leave one out
    y <- data[-i]
    M[i] <- func(y)
  }
  Mbar <- mean(M)
  se.jack <- sqrt(((n - 1)/n) * sum((M - Mbar)^2))
  return(se.jack)
}

```{r,eval=FALSE} jackafterboot <- function(data,func=NULL,B){ n <- length(data) theta.b <- numeric(B) # set up storage for the sampled indices indices <- matrix(0, nrow = B, ncol = n) # jackknife-after-bootstrap step 1: run the bootstrap for (b in 1:B) { i <- sample(1:n, size = n, replace = TRUE) y <- data[i] theta.b[b] <- func(y) #save the indices for the jackknife indices[b, ] <- i } #jackknife-after-bootstrap to est. se(se) se.jack <- numeric(n) for (i in 1:n) { #in i-th replicate omit all samples with x[i] keep <- (1:B)[apply(indices, MARGIN = 1, FUN = function(k) {!any(k == i)})] se.jack[i] <- sd(theta.b[keep]) } se.boot <- sd(theta.b) se.jackafterboot <- sqrt((n-1) * mean((se.jack - mean(se.jack))^2)) return(list(se.boot = se.boot, se.jackafterboot=se.jackafterboot)) }

In order to empirically compare _boot_ , _jack_ and _jackafterboot_, one generates 1,000 random numbers. The R code for comparing the three functions is as follows.

*In order to empirically compare _boot_ , _jack_ and _jackafterboot_, one generates 1,000 repicates of beta(2,3) * 20. *

*The R code for comparing the three functions is as follows.*

```{r}
data <- 20 * rbeta(1000,2,3)
(boot <- boot(data = data, B = 200, func = median)$se.b)
(jack <- jack(data = data, func = median))
(jackafterboot<- jackafterboot(data, B = 200, func = median))

As is shown in the result, standard error of jackafterboot is much lower than the result generated by bootstrap method. And you change the function and data, as is shown in the example, the standard error computed by jackknife-after-bootstrap is the lowest.

The method to download the package

{r,eval=TRUE} install.packages("devtools") devtools::install_github("lvli19/StatComp18096")

lvli19/StatComp18096 documentation built on May 5, 2019, 11:07 p.m.