Question

I want to run some maximum likelihood code on the data sample I have created. This is what I have so far:

library("maxLik") 
data <- replicate(20, rnorm(100))
logLikFun <- function(param) {
mu <- param[1]
sigma <- param[2]
sum(dnorm(data, mean = mu, sd = sigma, log = TRUE))
}
mle <- maxLik(logLik = logLikFun, start = c(mu = 0, sigma = 1))
summary(mle)

I am having some problems extracting the mean and standard deviation for each sample of the 20, I amended the apply function to try to suit this but nothing has worked yet. Any ideas?

Answer 1

Create a function (find.mle in this example) that takes a vector of data and calculates the MLE based on it, and then use apply to apply that to the columns of data:

library("maxLik") 
data <- replicate(20, rnorm(100))

find.mle = function(d) {
    logLikFun <- function(param) {
        mu <- param[1]
        sigma <- param[2]
        sum(dnorm(d, mean = mu, sd = sigma, log = TRUE))
    }
    maxLik(logLik = logLikFun, start = c(mu = 0, sigma = 1))$estimate
}

mles = apply(data, 2, find.mle)

This will give you a 2×20 matrix with your estimates:

> mles
            [,1]      [,2]        [,3]       [,4]       [,5]        [,6]
mu    0.03675611 0.1129927 -0.06499549 0.04651673 0.06593217 -0.08753828
sigma 0.93497523 0.9817961  0.84734600 0.93139761 1.01083924  1.04114752
           [,7]       [,8]      [,9]       [,10]      [,11]       [,12]
mu    0.1629807 0.01665411 0.2306688 -0.02147982 0.07723695 0.009476477
sigma 1.0428713 1.01658241 1.0073277  0.99781761 0.99327722 0.983356049
           [,13]      [,14]      [,15]      [,16]     [,17]     [,18]
mu    0.06524147 0.02442983 -0.1305258 -0.1050299 0.1449996 0.1172218
sigma 1.04004799 0.89963009  0.9979824  1.0227063 0.9319562 0.9916734
           [,19]       [,20]
mu    -0.1288296 -0.05769467
sigma  0.9975368  0.89506586