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Within a maximum likelihood context, the standard errors depend on the number of observations—the more observations we have, the smaller the standard errors will be (greater precision). As we can see in the following results, we get standard errors that are almost 50% of the estimated coefficients:

N <- 10x <- rgamma(N, shape=20,rate=2)LL <- function(shape, rate) {  R = suppressWarnings(dgamma(x, shape=shape, rate=rate))  return(-sum(log(R)))}P_10 = mle2(LL, start = list(shape = 1, rate=1))summary(P_10)

The estimated coefficients and standard errors (N=10) are as follows:

Estimate Std. error Z value p-value
Shape 13.76 6.08 2.24 0.02*
Rate 1.36 0.61 2.22 0.02*

 

The standard errors are much larger than before, almost ...

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