Obtain Bootstrap Results in Matrix - r

Question

I have written the following code.
library(quantreg)
# return the g function:
G = function(m, N, gamma) {
Tm = m * N
k = 1:Tm
Gvalue = sqrt(m) * (1 + k/m) * (k/(m + k))^gamma
return(Gvalue)
}
sqroot <- function(A) {
e = eigen(A)
v = e$vectors
val = e$values
sq = v %*% diag(sqrt(val)) %*% solve(v)
return(t(sq))
}
fa = function(m, N, a) {
Tm = m * N
k = 1:Tm
t = (m + k)/m
f_value = (t - 1) * t * (a^2 + log(t/(t - 1)))
return(sqrt(f_value))
}
m = 50
N = 2
n= 50*3
x1 = matrix(runif(n, 0, 1), ncol = 1)
x = cbind(1, x1)
beta = c(1, 1)
xb = x %*% beta
pr = 1/(1+exp(-xb))
y = rbinom(n,1,pr)
# calculate statistic:
stat = function(y, x, m, N, a) {
y_train = y[1:m]
x_train = x[(1:m),]
y_test = y[-(1:m)]
x_test = x[-(1:m),]
fit = glm(y ~ 0 + x, family="binomial")
coef = coef(fit)
log_predict = predict(fit, type="response")
sigma = sqrt(1/(m-1)* sum((y_train - log_predict)^2))
Jvalue = t(x_train) %*% x_train/m * sigma^2
Jsroot = sqroot(Jvalue)
fvalue = fa(m, N, a)
score1 = apply((x_test * as.vector((y_test - x_test %*% coef))), 2, cumsum)
statvalue1 = t(solve(Jsroot) %*% t(score1))/fvalue/sqrt(m)
statmax1 = pmax(abs(statvalue1[, 1]), abs(statvalue1[, 2]))
result = list(stat = statmax1)
return(result)
}
m =50
N = 2
a = 2.795
value = stat(y, x, m, N, a)
value
I want to perform bootstrap to obtain B = 999 number of statistics. I use the following r code. But it produces an error saying "Error in statistic(data, original, ...) :
argument "m" is missing, with no default"
library(boot)
data1 = data.frame(y = y, x = x1, m = m , N = N, a = a)
head(data1)
boot_value = boot(data1, statistic = stat, R = 999)
Can anyone give me a hint? Also, am I able to get the bootstrap results in a matrix format? Since the stat function gives 100 values.

Answer 1

There are different kinds of bootstrapping. If you want to draw from your data 999 samples with replications of same size of your data you may just use replicate, no need for packages.
We put the data to be resampled into a data frame. It looks to me like m, N, a remain constant, so we just provide it as vectors.
data2 <- data.frame(y=y, x=x)
stat function needs to be adapted to unpack y and x-matrix. At the bottom we remove the list call to get just a vector back. unnameing will just give us the numbers.
stat2 <- function(data, m, N, a) {
y_train <- data[1:m, 1]
x_train <- as.matrix(data[1:m, 2:3])
y_test <- data[-(1:m), 1]
x_test <- as.matrix(data[-(1:m), 2:3])
y <- data[, "y"]
x <- as.matrix(data[, 2:3])
fit <- glm(y ~ 0 + x, family="binomial")
coef <- coef(fit)
log_predict <- predict(fit, type="response")
sigma <- sqrt(1/(m-1) * sum((y_train - log_predict)^2))
Jvalue <- t(x_train) %*% x_train/m * sigma^2
Jsroot <- sqroot(Jvalue)
fvalue <- fa(m, N, a)
score1 <- apply((x_test * as.vector((y_test - x_test %*% coef))), 2, cumsum)
statvalue1 <- t(solve(Jsroot) %*% t(score1))/fvalue/sqrt(m)
statmax1 <- pmax(abs(statvalue1[, 1]), abs(statvalue1[, 2]))
result <- unname(statmax1)
return(result)
}
replicate is a cousin of sapply, designed for repeated evaluation. In the call we just sample the rows 999 times and already get a matrix back. As in sapply we need to transform our result.
res <- t(replicate(999, stat2(data2[sample(1:nrow(data2), nrow(data2), replace=TRUE), ], m, N, a)))
Result
As result we get 999 bootstrap replications in the rows with 100 attributes in the columns.
str(res)
# num [1:999, 1:100] 0.00205 0.38486 0.10146 0.12726 0.47056 ...
The code also runs quite fast.
user system elapsed
3.46 0.01 3.49
Note, that there are different kinds of bootstrapping. E.g. sometimes just a part of the sample is resampled, weights are used, clustering is applied etc. Since you attempted to use boot the method shown should be the default, though.