Pengantar Bootstrapping dalam R

Membuat Distribusi Normal Acak Menggunakan rnorm()

set.seed(300) # Setting the seed for replication purposes
myData <- rnorm(2000,20,4.5) # Creating a random normal distribution (n=300, mean=20, sd=4.5)

Melakukan Pemeriksaan Awal (Sanity Checks) pada myData Menggunakan length(), mean(), dan sd()

length(myData) # How many observations?
## [1] 2000
mean(myData) # What is the mean?
## [1] 20.25773
sd(myData) # What is the standard deviation?
## [1] 4.590852

Membuat Grafik untuk myData

# Membuat histogram dari myData
hist(myData, breaks = 30, col = "lightblue", main = "Distribusi myData", xlab = "Nilai", ylab = "Frekuensi")

# Menambahkan garis vertikal untuk mean
hist(myData, breaks = 30, col = "lightblue", main = "Distribusi myData", xlab = "Nilai", ylab = "Frekuensi")
abline(v = mean(myData), col = "red", lwd = 2, lty = 2)

# Menambahkan legenda
hist(myData, breaks = 30, col = "lightblue", main = "Distribusi myData", xlab = "Nilai", ylab = "Frekuensi")
abline(v = mean(myData), col = "red", lwd = 2, lty = 2)
legend("topright", legend = paste("Mean =", round(mean(myData), 5)), col = "red", lty = 2, lwd = 2)

Bootstrapping Menggunakan Fungsi Dasar R

Resampling dari myData Sebanyak 1000 Kali Menggunakan for(i in x)

set.seed(200) # Setting the seed for replication purposes
sample.size <- 2000 # Sample size
n.samples <- 1000 # Number of bootstrap samples
bootstrap.results <- c() # Creating an empty vector to hold the results
for (i in 1:n.samples)
{
 obs <- sample(1:sample.size, replace=TRUE)
 bootstrap.results[i] <- mean(myData[obs]) # Mean of the bootstrap sample
}
length(bootstrap.results) # Sanity check: this should contain the mean of 1000 different samples
## [1] 1000
summary(bootstrap.results) # Sanity check
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   19.92   20.19   20.26   20.26   20.33   20.57
sd(bootstrap.results) # Checking the standard deviation of the distribution of means (this is what we are interested in!)
## [1] 0.1021229
par(mfrow=c(2,1), pin=c(5.8,0.98)) # Combining plots (2 rows, 1 column) and setting the plots size
hist(bootstrap.results, # Creating an histogram
col="#d83737", # Changing the color
xlab="Mean", # Giving a label to the x axis
main=paste("Means of 1000 bootstrap samples from myData")) # Giving a title to the graph

hist(myData, # Creating an histogram
col="#37aad8", # Changing the color
xlab="Value", # Giving a label to the x axis
main=paste("Distribution of myData")) # Giving a title to the graph

Pengambilan sampel ulang sebanyak 1000 kali dari proses pembuatan data aktual menggunakan for(i in x)

set.seed(200) # Setting the seed for replication purposes
sample.size <- 2000 # Sample size
n.samples <- 1000 # Number of bootstrap samples
bootstrap.results <- c() # Creating an empty vector to hold the results
for (i in 1:n.samples)
{
 bootstrap.results[i] <- mean(rnorm(2000,20,4.5)) # Mean of the bootstrap sample
}
length(bootstrap.results) # Sanity check: this should contain the mean of 1000 different samples
## [1] 1000
summary(bootstrap.results) # Sanity check
##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##   19.64   19.93   20.00   20.00   20.07   20.32
sd(bootstrap.results) # Checking the standard deviation of the distribution of means (this is what we are interested in!)
## [1] 0.1041927
par(mfrow=c(2,1), pin=c(5.8,0.98)) # Combining plots (2 rows, 1 column) and setting the plots size
hist(bootstrap.results, # Creating an histogram
col="#d83737", # Changing the color
xlab="Mean", # Giving a label to the x axis
main=paste("Means of 1000 bootstrap samples from the DGP")) # Giving a title to the graph

hist(myData, # Creating an histogram
col="#37aad8", # Changing the color
xlab="Value", # Giving a label to the x axis
main=paste("Distribution of myData")) # Giving a title to the graph